Action Research & TPD Project

                                                          

 

 TPD Model

======================= sf7df8f} sf] sIff ( sf laBfyL{x?df ul/Psf]

lahul0ft cGtu{t vl08s/0f ;DalGw

sfo{d"ns cg';Gwfg

@)=====

 

                                     

 

 

 

 

 

 

Zf}lIfs tflnd s]Gb| lqk'/]Zj/ sf7df8f} / cu'jf ;f]|ts]Gb| ==========sf] cfof]hgfdf ;DkGg lzIfssf] k];fut lasf; (TDP) ;DaGwL

bz lbg] k|ToIf e]63f6 tflndkl5 :jfWoog v08df tof/ kfl/Psf]

k|lta]bg

 

 

 

 

                             k|:t'tstf{{ M

                    lz=;s]]t g+=M

                                    tx  M dfWolds

                                     laifo M ul0ft

                              laBfno M

 

 

laifo;'rL

klxnf] efu

!= kl/ro M

@= ;d:of M

#= ;d:ofsf] klxrfg M

$= cWoogsf p2]Zox? M

%= sf/0fx? M

^= ;dfwfgsf pkfox? M

&= lg/fs/0fsf] k|fyldstf M

bf];f]| efu

s= pkfox? M

v= sfof{Gjog M

u= cjnf]sg M

3= k|ltljDjg

ª= lgisif{ M

cg';'rL

 

 

 

 

 

 

 

 

 

 

klxnf] efu

!= kl/ro M

           lzIfssf] k];fut ljsf; (TDP) cGt/utsf] ldlt @)===÷)@÷) ut] b]lv @)==÷)@÷== ;Dd bzlbg] sfo{zfnfkZrft\ cfˆgf] k];fut Ifdtf clea[l4 ug{] l;nl;nfdf lzIffsf] k];fut lasf; tflndsf] kGwlbg] k'/s sfo{sf] ?kdf /x]sf] bf];|f] efu -:jfWoog v08_ cGt/ut of] cg';Gwfg ul/Psf] xf] . lzIffsf] x}l;otn] cfkm'n] cWofkg ubf{ sIffsf]7fleq ul/g] lqmofsnfk4f/f ljifout pknlAw k|ltzt a[l4 ug]{ ;afndf k6sk6s laleGgvfn] ;d:ofx? cfOkg]{ x'G5 . tL ;d:of ;dfwfg ug{ oyf;Dej pkfo / k|of;x? lzIfs :jod\n] :jLsfg{' kg{] x'G5 . ;–;fgf ;d:of / ltgsf pTkltsf sf/0f kQf nufO{ ltgsf] lg/fs/0f ug{ ;s] lzIf0f k|efjsf/L / ck]lIft pknlAw kfpg ;lsG5 . ToxL s|ddf lzIfs :jod\ ;lqmo eO{ cfˆgf ljifout ;d:ofx?sf] ;dfwfgsf nfuL ul/g] 5f]6f–5f]6f jf cNksfnLg cg';Gwfg g} sfo{d'ns cg';Gwfg xf] .

           ul0ft lzIfssf] x}l;otn] sIffdf lzIf0f ubf{ k6sk6s ;d:ofx?sf] ;fdgf ug'{kg{] x'G5 . c+sul0ft, lahul0ft, HofldtL, tyf+szf:q, lqsf]0fldtL, ;+efAotf h]xf];\ tL ;a}df s'g} g s'g} ?kdf ;d:of cfO g} /xG5g\ . hlt;'s} /fd|/L / hlt;'s} :ki6tf ;fy ljljw pbfx/0f ;d]tsf] k|of]u u/fP/ klg laBfyL{x?n] /fd|/L a'‰g g;Sg], a''em]sf s'/f /fd|/L :yfgfGt/0f ug{ g;Sg], rfF8} la;{g] / k9fO-l;sfO_ k|lt g} g}/fZo b]vfpg] cflb ;d:ofx? s'g} g s'g} ?kdf s'g} g s'g} laBfyL{df cfO g} /xG5 . o; cy{df dnfO{ ljljw ;d:ofn] hlxn] klg ;tfO /xG5g\ . o;} ;Gbe{df lahul0ft lzIf0fsf qmddf vl08s/0fsf] cEof; u/fpFbf b]vf k/]sf ;d:ofsf] ;dfwfgsf lgldQ sfo{d'ns cg';Gwfg pko'Qm x'g] s'/f cg'ej u/L of] ljifo r'lgPsf] xf] .

@= ;d:of M

           dfWolds txsf] sIff gf} / b;df sIff sfof{snfk u/fpFbf lahul0ft cGt/ut vl08s/0f ug{ g;Sg] ;Lksf] cefj b]lvPsfn] laBfyL{x?sf] k|of]Tds ;Lk clea[l4sf nflu ;do;do sIffdf laBfyL{x?nfO{ pQm sfo{ u/fpFbf laBfyL{ :j+dnfO{ ;lqmo gx'g], cfkm}Fn] klg cEof; u/fpFbf ;d]t laBfyL{x?dWo] Ps b'O{ hgf afx]s ug{ g;s]sf] ljutsf] k6sk6ssf] cg'ejn] of] ;d:of ;dfwfg ug{ jf o;df k|z:t ;'wf/ ug{  o;nfO{ ;d:ofsf] ?kdf lnOPsf] 5 . ;fgf] / uf}0f nfUg] of] ;d:ofn] laBfyL{x?sf] lahul0ft cGt/ut vl08s/0f ;DaGwL cle?lrnfO{ gsf/fTdstf lt/ nfg] u/]sfn] laBfyL{x? lahul0ft cGt/ut vl08s/0fdf hlt /Dg'kg]{ xf] TotL hfu?s gb]lvg' ul0ft lzIf0fdf b]lvPsf] Pp6f ;d:of xf] eGg ;lsG5 .

#= ;d:ofsf] klxrfg M

           cfˆgf] cWofkg sfo{sf] nfdf] cGt/fn kZrft\ klg o;nfO{ ;d:ofsf] ?kdf lnPsf] lyOg . vf;ul/ d lahul0ftsf laifoa:t'sf]  lzIf0f u/]/ vf;} ;Gt'i6 x'g ;lsg . laBfyL{x?nfO{ klg kl/Iffdf laifout 1fgn] dfq geO Aofaxfl/s / k|of]ufTds kIfn] klg laBfyL{sf] Ifdtfdf clea[l4 x'G5, x'b}Fg cgle1 g} /lxof] t/ kl5kl5 ha laBfyL{x?sf] ;xefuLtfdf sIffdf z}Ifl0fs ls|ofsnfk ;'? ug{ nfu]F To;kl5 eg] lahul0ft cGt/ut vl08s/0f nfO{ g} k|fyldstf lbg yfFn] . o;af6 laBfyL{x?df lahul0ft cGt/ut vl08s/0f ug{ grfxg] / /fd|f];Fu cle?rL lbg g;Sg] ;d:of k|z:t /x]sf] kfOof] . o;n] laBfyL{x?df ul0ft lzIf0f ljsf;df 7'n} afwf pTkGg u/fPsf] :ki6 eof] . ;fy} o;n] laBfyL{x?sf] cleJolQm Ifdtfdf x|f; ePsf] b]lvof] . o:tf] ;d:ofaf/] cGo ul0ft laifosf lzIfs;Fusf] s'/fsfgLsf qmddf sIff * sf laBfyL{x?df o:t} ;d:of /x]sf] / o;sf] ;dfwfgsf lglDt  s]xL k|of; u/]sf] klg kfOof] . o;/L ul0ft lzIf0fdf b]lvPsf] o; k|sf/sf] ;d:of d]/f] nfuL laBfyL{x?nfO{ k|of]ufTds / Aofaxfl/s lzIf0f u/fpg ;d:ofsf] ?kdf b]lvof] .

$= cWoogsf p2]Zox? M

   s= ul0ft lzIf0f cGt/ut vl08s/0fdf laBfyL{sf] ?lr hufpg] .

   v= ;d:ofsf] sf/0f kQf nufO{ ;dfwfg vf]Hg] .

   u= k|of]ufTds / Aofaxfl/s ?kdf ;d:of ;dfwfg ug{ ;Sg] agfpg] .

%= sf/0fx? M

    d}n] ul0ft lzIf0f cGt/ut vl08s/0fdf laBfyLnfO{  ;d:of ;dfwfg ug nufpFbf  laBfyL{x?n] /fd|f]  ug{ ;s]gg\ . o;sf sf/0fx? lgDg x'g;S5g\ .

   s= laBfyL{x?sf] dfgl;stfdf ul0ft lzIf0f ;DaGwL wf/0ff g} ga:g' .

   v= cEof;x?df sld x'g' .

   u= >Job[Zo ;fdfu|Lsf] k|of]u gx'g' .

   3= ul0ft ljifoeGbf cGo ljifonfO{ a9L dxTj lbg' .

^= ;fdfwfgsf pkfox? M

   dfly % g+= df pNn]v ul/Psf] ;d:of ;dfwfgsf nflu lgDgfg';f/ pkfpx? canDag ug{ ;lsG5 .

   s= ljBfyL{x?nfO{ ;lqmo agfO{ af/Daf/ ;d:of ;dfwfg ug{ pT;flxt ug{], xf};nf a9fO{ pgLx?sf] cfTdan a9fpg] .

   v= lzIfs :jodn], z}lIfs ;fdfu|Lsf] k|of]un] jf cfkm}Fn] cfudg / lgudg lalw k|of]u ul/ ul0ft lzIf0fdf laBfyL{nfO{ cfslif{t / clek|]l/t ug{] .

    u= sIff 6]i6 jf ul0ft k|ltof]lutf u/L pTs[i6nfO{ k'/is[t ug{], o:tf] sfo{qmd sIffut / laBfno:t/d}F rnfpg] .

   3= ljifout ?kdf ul0ftsf] dxTj cGo ljifoeGbf sd 5}g eGg] efjgf hufpg] .

&= lg/fs/0fsf] k|fyldstf M

   != ljBfyL{x?nfO{ ;lqmo agfO{ af/Daf/ cEof; u/fO{ cEo:t agfpg] .

   @= lzIfs cfkm}Fn] cfudg / lgudg lalw k|of]u ul/ laBfyL{nfO{ k6sk6s 5nkmn ub{} cEof; u/fpg] .

 

 

 

 

 

bf];f]| efu

sfo{d"ns r/0f

s= pkfox? M

   ul0ftdf vl08s/0f lzIf0fdf cg';Gwfgsf] s|ddf s] b]lvof] eg] cEof; g} ;a}eGbf dxTj k'0f{ tTj xf] . ul0ftdf vl08s/0 lzIf0fdf ljBfyL{x?nfO{ hlt cEof; u/fpg ;Sof] Tolt g} cAan x'g] /x]5g . sIff ( sf] kf7\ok':tsdf ePsf cEof;nfO{ cfudg / lgudg lalwaf6 5nkmn ub{} ;d:of ;dfwfg ug{'kb{5  . o;af6 s] b]lvof] eg] 7'nf7'nf l;4fGtsf s'/f 5f]8]/ cEof;df k|of]ufTdstdf laz]if Wofg lbOof] eg] ljBfyL{x?df pgLx?sf] Ifdtf k|:km'6g u/fpg ;lsG5 . o;sf] nflu slxn] < sxfF < s] < s;n] < slt ;dodf < eGg] s'/f k|:6 x'g cfjZos 5 .

v= sfof{Gjog M

   dfly …sÚ df k|:t't ul/Psf] of]hgfadf]lhd g} sfof{Gjog eof] . Tof] k|ls|of lg/Gt/ rNg] ePsfn] kl5Nnf vl08s/0f lzIf0fsf s|ddf ckgfOFb}  uOof] . t/ klg ;do ;Ldfsf sf/0f oy]i6 cEof; u/fpg eg] ;lsPg / sIffsf]7fafx]ssf nflu pko'Qm jftfj/0f ldn]g h;n] ubf{ sIffafx]ssf] ;dodf ljBfyL{x?nfO{ vl08s/0f lzIf0f u/fpg] cj;/ k|fKt ePg . t/ klg u[xsfo{sf ?kdf eP klg cEof;df a[l4 ul/of] .

u= cjnf]sg M

   sfof{Gjogsf] l;nl;nfdf hl6ntf / Jojwfgx? k|z:t eP . ;'?;'?df sIffdf k|ofKt cEof; ug{ ljBfyL{x? tof/ gx'g] / eP klg Psfb'O{ k|Zg eGbf a9L xn ug{ tof/ gx'g] tyf s;}n] xn u/Lxfn] klg ldnfpg g;Sg] ;d:ofx? cfP t/ lg/Gt/sf] cEof;n] la:tf/} s]xL laBfyL{x?df ?lr b]vfpg], k9g\ k|of; ug{], uNtL af sdhf]/L klxNofO{ To;nfO{ ;'wfg{] x'b}F uP . sIffsf ;a}n] ;d'xut / JolQmut ?kd} ;lqmotf b]vfP, lg/Gt/sf] k|of; lgs} ;'wf/ ePsf] kfOof] . sfof{Gjogn] ljBfyL{x?df ;lqmotf a9fof], xf};nf k|bfg u¥of] / plgx? To; k|sf/sf] sfddf pT;fxk'j{s efu lng] eP . sIffsf Psfwafx]s k|foM ;a}n] o;nfO{ /fd|f] u/]/ b]vfP . o;n] ck]lIft l;sfO pknAlw xfl;n ug{ ;sf/fTds k|efj kf/]sf] kfOof] .

3= k|ltlaDag M

   jf:tjdf sfo{d'ns cg';Gwfgn] ;d:ofsf] klxrfg ul/ s'g} klg lawfdf k/]sf, cfPsf] ;d:of ;dfwfg u/L lzIf0f k|s[ofnfO{ cl3 a9fpg ;lsG5 eGg] s'/f a'lemof] . sfo{d'ns  cg';Gwfgn] lzIfs / ljBfyL{ b'j} kIfnfO{ ;hutf jf nfe k'¥ofpg] ePsfn] o:tf] cg';Gwfg lg/Gt/ ul//xg' kg{] b]lvG5 . o:tf] k|s[ofaf6 k|fKt lgisif{ cGo ;xefuL lzIfs jf ;DjlGwt ;/f]sf/afnfx?nfO{ klg ;'gfpg ;lsG5 . o;af6 laBfyL{ lzIfs / cleefjs lqkIfLo nfe x'g] s'/fnfO{ s;}n] gsf{g ;Sb}g\ .

ª= lgisif{ M

   sfo{d"ns cg';Gwfg lzIfsn] cfˆgf] lzIf0f k|s[ofdf cfOk/]sf ljifo, ljwf jf lzif{sdf lglxt x'G5 . of] cg';Gwfg lg/Gt/ rln/xsg] k|s[of xf] . ljBfyL{n] s;/L a'‰g ;S5g eg]/ lzIfsn] ckgfpg] tl/sf 9fFrf jf sfo{ g} cg';Gwfg xf] . sxfF s] s] sf] sdL 5 < eGg] k|Zg sf] pQ/sf] ?kdf sfo{d'ns cg';Gwfg cfPsf] x'g'k5{ .  

 

cg';'rL

b}lgs kf7of]hgf !

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

s_  eg]sf] au{ xf] eGg] wf/0f lbg] .

v_  o;sf] nDafO{ / rf}8fO{ qmdzM (a +b)  / (a +b) 5 eGg] wf/0ff lbg] .

u_ (a +b)²  = a²+2ab+b²  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, auf{sf/ sfuh cfbL .

#=lqmofsnfkM

s_ (a +b) e'hf ePsf] au{ lgdf{0f u/L k|To]s au{ / cfotsf] If]qkmn hf]8\g] .

v_ au{ ABCD sf] If]qkmn = (AEGI + EBsHG + GHCF + IGFD ) sf]If]qkmn

         = a×a + a×b +b×b + a×b

            = a²+2ab+b²                                                     a              b

                                                         a

 

                                                         b

$=d"NofÍg M

  Kf'gM laBfyL{x?nfO{ canf]sg ug{ nufO{ 5'6\ofpg nufpg], o;/L klg x]g{ nufpg] h;df b'O{j6f au{ / b'O{j6f cfot 5g\ . cGtdf ;DalGwt cGo ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf @

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

s_  a² au{af6 nDafO{, rf}8fO{ (a -b) agfpg] wf/0f lbg .

v_  (a -b)²  = a²-2ab+b²  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, auf{sf/ sfuh cfbL .

#=lqmofsnfkM

s_ a e'hf ePsf] au{ lgdf{0f u/L  auaf6  cfotsf] If]qkmn 36fpg nufpg] .

v_ au{ AEGI sf] If]qkmn = (ABCD - EBHG - GHCF - IGFD ) sf]If]qkmn

         (a -b)²= a ² - b(a -b) -b(a -b)² -b×b

            = a²-2ab+b²                                                                      b

                                

                                                   a

                                                         b

$=lgisif{ -d"NofÍg_M                                                         a

  K f'gM laBfyL{x?nfO{ canf]sg ug{ nufO{ 5'6\ofpg nufpg], o;/L klg x]g{ nufpg] h;df b'O{j6f au{ / b'O{j6f cfot 5g\ . cGtdf cGo ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf #

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ o;sf] nDafO{, rf}8fO{ / prfO{ a/fa/ ePsf] 7f]; xf] h;sf] nDafO{, rf}8fO{ / prfO

  (a +b)  5 eGg] wf/0ff a;fNg .

  v_ (a +b)³ = a³+3a²b+ 3ab²+b²  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, 3gfsf/ 7f]; a:t' cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ 3g eg]sf] nDafO{, rf}8fO{ / prfO{ a/fa/ ePsf] 7f]; xf] h;sf] nDafO{, rf}8fO{ / prfO{ (a +b) g} 5 eGg] wf/0ff laBfyL{df a;fNg] .

v_ laBfyL{x?nfO{ cfotg lgsfNg  L×B ×H x'g] ePsfn] (a +b)³= L×B ×H

  = (a +b) (a +b) (a +b) u'0fg u/L a³+3a²b+ 3ab²+b²  agfpg nufpg] .         

$=lgisif{ M

  laBfyL{nfO{ pQm tYo ;To jf c;To kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

 

b}lgs kf7of]hgf $

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + 3a df b'O{ klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] au{ / csf{] nDafO{ a / rf}8fO{ 1 EfPsf] tLg cf]6f cfot ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ a²  ePsf] Pp6f au{ / a ×1 sf] tLg cf]6f cfot lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a e'hf ldNg] u/L cfot hf]8\g] .    

u_ 7"nf] cfotsf] If]qkmn lgsfNg] .   

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf laBfyL{x?nfO{ cEof;Fu ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf %

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + 5a+6 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] kfFr cf]6f cfot tyf 1 au{ PsfO{sf ^ cf]6f au{ ePsf] wf/0f b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] kfFr cf]6f cfot tyf 1 au{ PsfO{sf ^ cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1sf cfot / 1×1 sf au{x? ldNg] u/L hf]8\g nufpg].   

u_ 7"nf] cfotsf] If]qkmn lgsfNg] .        

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

 

b}lgs kf7of]hgf ^

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + 6a+5 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] ^ cf]6f cfot tyf 1 au{ PsfO{sf % cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] ^ cf]6f cfot tyf 1 au{ PsfO{sf % cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1sf cfot / 1×1 sf au{x? ldNg] u/L hf]8\g nufpg].   

u_ 7"nf] cfotsf] If]qkmn lgsfNg] .        

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf &

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + 2a+3 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] kfFr cf]6f cfot tyf 1 au{ PsfO{sf ^ cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] @ cf]6f cfot tyf 1 au{ PsfO{sf # cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1sf cfot / 1×1 sf au{x? ldNg] u/L hf]8\g nufpg].   

u_ 7"nf] cfotsf] If]qkmn lgsfNg] .        

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg d"NofÍg ug'{ kb{5 .

 

b}lgs kf7of]hgf *

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² - a - 6 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] Pp6f cf]6f cfot tyf 1 au{ PsfO{sf ^ cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] Pp6f cf]6f cfot tyf 6 au{ PsfO{sf ^ cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1 sf cfot / 1×1 sf au{x? ldNg] u/L cfaZostf cg';f/ hf]8\g / 36fpg nufpg] .

u_ cfaZos cfotsf] If]qkmn lgsfNg] .    

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf (

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + a - 2 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] Pp6f cf]6f cfot tyf 1 au{ PsfO{sf @ cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] Pp6f cf]6f cfot tyf 1 au{ PsfO{sf @ cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1 sf cfot / 1×1 sf au{x? ldNg] u/L cfaZostf cg';f/ hf]8\g / 36fpg nufpg] .

u_ cfaZos cfotsf] If]qkmn lgsfNg] .    

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

b}lgs kf7of]hgf !)

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² + 2a - 3 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] @ cf]6f cfot tyf 1 au{ PsfO{sf # cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] @ cf]6f cfot tyf 1 au{ PsfO{sf # cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1 sf cfot / 1×1 sf au{x? ldNg] u/L cfaZostf cg';f/ hf]8\g / 36fpg nufpg] .

u_ cfaZos cfotsf] If]qkmn lgsfNg] .    

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

b}lgs kf7of]hgf !!

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² -a - 12 df ax'klbo cleAo~hs EfPsf] wf/0ff lasf; ug{ .

  v_ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] ! cf]6f cfot tyf 1 au{ PsfO{sf !@ cf]6f au{ ePsf] wf/0f  b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² ePsf] Pp6f au{,  csf{] nDafO{ a / rf}8fO{ 1 EfPsf] ! cf]6f cfot tyf 1 au{ PsfO{sf !@ cf]6f au{ lgdf{0f ug{] .

v_ laBfyL{x?nfO{ a² sf] au{df a×1 sf cfot / 1×1 sf au{x? ldNg] u/L cfaZostf cg';f/ hf]8\g / 36fpg nufpg] .

u_ cfaZos cfotsf] If]qkmn lgsfNg] .    

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

b}lgs kf7of]hgf !@

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of 2a² + 7ab +5b² df u'0fg ubf{ 10 / hf]8\bf 7 x'g] ;+Vof cfaZos kg{]] wf/0ff lasf; ug{ .

  v_ o;df a²  / b² ePsf] au{x? qmdzM @ / % j6f tyf & j6f cfot ePsf] wf/0ff lbg .

u_  e'hf a / b ePsf au{ tyf nDafO{ a / rf}8fO{ b EfPsf] ;ft cf]6f cfot ldnfO{ gofF cfot lgdf{0f u/L b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² / b² ePsf] au{ tyf  nDafO{ a / rf}8fO{ b EfPsf] ;ft cf]6f cfot hf]8]/ gofF cfot lgdf{0f ug{ nufpg] .

v_ lbOPsf] ;d:of 2a² + 7ab +5b² df u'0fg ubf{ 10 / hf]8\bf 7 x'g] ;+Vof tflnsfsf] ;xfotfaf6 kQf nufpg]

a×b=10	a+b =7
10×1 -10×-1  2×5	10+1 -10-1 2+5=7

 

u_ laBfyL{x?nfO{ dflysf] tflnsfaf6 pko"Qm kb 5gf]6 ug{ nufpg] 2a²+7ab+5b²= 2a²+(2+5)ab+5b²   

3_ cfaZos cfotsf] If]qkmn lgsfNg] .       

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

b}lgs kf7of]hgf !#

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of 5a² -8a -4 df u'0fg ubf{ -20 / hf]8\bf -8 x'g] ;+Vof cfaZos kg{]] wf/0ff lasf; ug{ .

  v_ o;df a²   ePsf] au{  % j6f tyf nDafO{ a / rf}8fO{ 1 PsfO{ ePsf * j6f cfot tyf 1 au{ PsfO{ ePsf $ cf]6f au{sf] wf/0ff lbg .

u_  e'hf a / 1  PsfO{ ePsf au{ tyf nDafO{ a / rf}8fO{ 1 EfPsf] cf7 cf]6f cfot ldnfO{ gofF cfot lgdf{0f u/L b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² / 1² ePsf] au{ tyf  nDafO{ a / rf}8fO{ 1 EfPsf] cf7 cf]6f cfot hf]8]/ gofF cfot lgdf{0f ug{ nufpg] .

v_ lbOPsf] ;d:of 5a² -8a -4 df u'0fg ubf{ -20 / hf]8\bf -8 x'g] ;+Vof tflnsfsf] ;xfotfaf6 kQf nufpg] .

a×b=-20	A+b =-8
-20×1 20×-1 10×-2 -10×2  -4×5 -5×4	-20+1 20+-1 10+-2 -10+2=-8  -4+5 -5+4

 

u_ laBfyL{x?nfO{ dflysf] tflnsfaf6 pko"Qm kb 5gf]6 ug{ nufpg] 5a²-8a-4 = 2a²+(2-10)a-4    

3_ cfaZos cfotsf] If]qkmn lgsfNg] .   

$=lgisif{ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

b}lgs kf7of]hgf !$

klxnf] r/0fM ;d:of klxrfg

 s_ 3ftfÍ ;DalGw wf/0ff lbg] .

 v_ L.C.M. lnO{ vl08s/0f ug{'kg{] wf/0ff lbg] .

bf];|f] r/0fM of]hgf lgdf{0f

laBfyL{;Fu 5nkmn lalwaf6 L.C.M. lng], qm; u'0fg u/L vl08s/0f ug{] .

t];|f] r/0f M of]hgf sfof{Gjog

4^x+1/4^x  =  17/4

…………….

…………….

X=+2

Rff}yf] r/0fM laBfyL{nfO{ pko"Qm xn l7s eof] ePg x sf] dfg /flv hfFRg nufpg' kb{5 . cGtdf laBfyL{nfO{ ;DalGwt cGo ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

b}lgs kf7of]hgf !%

!= lalzi6 pb]ZoM of] kf7sf] cGtdf laBfyL{x? lgDg s'/fdf ;Ifd x'g]5gM

  s_ lbOPsf] ;d:of a² +3a -4 df u'0fg ubf{ -4 / hf]8\bf 3 x'g] ;+Vof cfaZos kg{]] wf/0ff lasf; ug{ .

  v_ o;df a²   ePsf] au{ ! j6f tyf nDafO{ a / rf}8fO{ 1 PsfO{ ePsf # j6f cfot tyf 1 au{ PsfO{ ePsf $ cf]6f au{sf] wf/0ff lbg .

u_  e'hf a / 1  PsfO{ ePsf au{ tyf nDafO{ a / rf}8fO{ 1 EfPsf] cf7 cf]6f cfot ldnfO{ gofF cfot lgdf{0f u/L b]vfpg .

@= z}lIfs ;fdfu|LM k]gl;n, s}rL, k]k/ cfbL .

#= lqmofsnfkM

s_ ;a{k|yd laBfyL{x?nfO{ o;df a² / 1² ePsf] au{ tyf  nDafO{ a / rf}8fO{ 1 EfPsf] cf7 cf]6f cfot hf]8]/ gofF cfot lgdf{0f ug{ nufpg] .

v_ lbOPsf] ;d:of 5a² +3a -4 df u'0fg ubf{ -4 / hf]8\bf 3 x'g] ;+Vof tflnsfsf] ;xfotfaf6 kQf nufpg] .

a×b=-4	a+b =3
1×-4 4×-1 2×-2	1-4 4-1=3 2-2

 

u_ laBfyL{x?nfO{ dflysf] tflnsfaf6 pko"Qm kb 5gf]6 ug{ nufpg] a²+3a-4 = a²+(2-1)a-4

3_ cfaZos cfotsf] If]qkmn lgsfNg] .    

$=lgisif{ -d"NofÍg_ M

  laBfyL{nfO{ pQm tYo kl/If0f ug{ nufpg] . cGtdf ;DalGwt cGo ;d:ofx? ;dfwfg ug{ nufpg' kb{5 .

 

Click here  :  Action Research : By J.B. sir  

Download : Action Research Report(NT)