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do clW vwly ryKI smIkrx

This document explores various methods for solving complex algebraic equations, offering step-by-step examples and strategies. It delves into quadratic equations, linear functions, and polynomial expressions, demonstrating how to manipulate and simplify them effectively. The content is designed for students and educators aiming to enhance their mathematical problem-solving skills, providing insights into variable manipulation and the application of theorems. By understanding these techniques, learners can approach algebra with greater confidence and proficiency.

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do clW vwly ryKI smIkrx

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  1. do clWvwlyryKIsmIkrx klws : nOvIN AiDAwie : pihlw mnpRIqisMG mYQmwstr s.h.sig`l (luiDAwxw)

  2. pUrvigAwx • ie`k Gwq qo kI Bwv hY? • cl qo kI Bwv hY? • ie`k cl qo kI Bwv hY? • kI qusIN do clW vwly ryKI smIkr bwry jwxdy ho? AwE bic`E A`j AsIN do clW vwly ryKI smIkr bwry jwxgyN[

  3. jwx pCwx • smIkrx ie`k AijhI smwnqw nUM ikhw jWdw hY ijs iv`c ie`k jW v`D AigAwq rwSIAW AwaudIAW hox , iehnw rwSIAW nMU cl ikhw jWdw hY [ • jdoN iksy smIkrx iv`c kyvl ie`k hI cl hovy qW ies cl dI Gwq 1 hovy qw Aijhw smIkrx ie`k cl vwlw smIkrx khwauNdw hY[

  4. ie`k cl vwlw smIkrx ies qrHW dw huMdw hY[ • ax+ b + 0,a≠0 • X=− ieh ryKI smIkrx dw h`l hY[ • audwhrx dy qOr qy: • 3x +4=5,2x+5= x+9, • (x-2)²=x²+1; ieh swry smIkrx ie`k cl vwly ryKI smIkrx hn[ b a 3 2

  5. iehnW swrIAW smIKrxw iv`c koeI vI ie`k cl vwlw ryKI smIkrx nhIN hY[ 1 u • x =+2 = x²-1, (x-2) (x+1) = 3.u + = 5

  6. ie`k cl vwly smIkrx dw h`l • cl dw ie`k Aijhw mu`l , ijhVw vwsqivk sMiKAw dy rUp iv`c hovy Aqy ijs nwl smIkrx dy dovyN pwsy brwbr ho jwx,smIkrx dw h`l AKvwauNdw hY[ • audwhrx leI • smIkrx 3x+4 =−5 iv`c • jdoN AsIN x dI QW qy -3 lYNdy hW qW, swnUM pRwpq huMdw hY • K`bw pwsw = 3(-3)+4= -9 +4= -5= s`jw pwsw • ikauNik x=-3 leI K`bw pwsw = s`jw pwsw (-5) hn, • ies leI ‘-3’ smIkrx 3x+4=-5 dw h`l hY[

  7. smIkrx dw h`l pqw krn leI hyT ilKy inXmW dI vrqoN kIqI jWdI hY[ • ie`ko ijhI rwSI nUM dovyN pwsy joVn qy smwnqw nhIN bdldI[ • ie`ko ijhI rwSI nUM dovyN pwsy qoN Gtwaux qy smwnqw nhIN bdldI[ • ie`ko ijhi rwSI (≠ 0 nw isPr) duAwrw dovyN pwisAW nUM guxw krn qy smwnqw nhIN bdldI[ • ie`ko ijhi rwSI (≠ 0 nw isPr) duAwrw dovyN pwisAW nUM Bwg krn qy smwnqw nhIN bdldI[

  8. sQwn pirvrqx • ie`k pwsy qoN ie`k pd AidRSt ho ky dUsr pwsy bdly hoey icMnHW nwl jdoN pRgt hovy qW ies ikirAw nUM sQwn pirvrqx kihMdy hn[ • audwhrx 1: smIkrx 5x +9 = 2x + 21 nUM h`l kro[

  9. sQwn pirvrqx • h```````l: swnUM id`qw hY: • 5x+9= 2x + 21 • 5x+9+(-9)=2x+21+(-9) dovyN pwisAW iv`c -9 joVn qy • 5x=2x+12 • 5x-2x=2x+12-2x [dovyN pwsy 2x Gtwaux qy] • 3x =12 • x=4 [ dovy pwsy 1/3 nwl guxw krn qy] • ies leI, x=4 id`qy gey smIkrx dw h`l hY[

  10. AiBAws

  11. hl kro • X=2,y=5 (2x-3y=-11) • X=2,y=5 (5x+3y=4)

  12. iehnWsmIkrnwnUMgrwPduAwrwsulJwE • X=4 • Y=-3 • X=0 • 3y-15=0 • X-y=0

  13. sRoq: pMjwb skUl is`iKAw borf dI novIN SRyxI dI pwT-pusqk, www.heathersanimations.com www.google.com

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