Question
Thu April 02, 2015 By: Rohith Kumar

 , Question no 89481, Mathematics
 

Expert Reply
Vimala Ramamurthy
Fri April 03, 2015
open parentheses 1 close parentheses C o n s i d e r space t h e space g i v e n space e q u a t i o n colon a squared b squared x squared plus b squared x minus a squared x minus 1 equals 0 B y space u sin g space q u a d r a t i c space f o r m u l a comma space w e space h a v e comma x equals fraction numerator negative open parentheses b squared minus a squared close parentheses plus-or-minus square root of open parentheses b squared minus a squared close parentheses squared minus 4 a squared b squared cross times open parentheses negative 1 close parentheses end root over denominator 2 a squared b squared end fraction space space space equals fraction numerator a squared minus b squared plus-or-minus square root of b to the power of 4 minus 2 a squared b squared plus a to the power of 4 plus 4 a squared b squared end root over denominator 2 a squared b squared end fraction space space space equals fraction numerator a squared minus b squared plus-or-minus square root of b to the power of 4 plus 2 a squared b squared plus a to the power of 4 end root over denominator 2 a squared b squared end fraction space space space equals fraction numerator a squared minus b squared plus-or-minus square root of open parentheses a squared plus b squared close parentheses squared end root over denominator 2 a squared b squared end fraction space space space equals fraction numerator a squared minus b squared plus-or-minus open parentheses a squared plus b squared close parentheses over denominator 2 a squared b squared end fraction rightwards double arrow x equals fraction numerator a squared minus b squared plus a squared plus b squared over denominator 2 a squared b squared end fraction space o r space x equals fraction numerator a squared minus b squared minus a squared minus b squared over denominator 2 a squared b squared end fraction rightwards double arrow x equals fraction numerator 2 a squared over denominator 2 a squared b squared end fraction space o r space x equals fraction numerator negative 2 b squared over denominator 2 a squared b squared end fraction rightwards double arrow x equals 1 over b squared space o r space x equals fraction numerator negative 1 over denominator a squared end fraction P l e a s e space c h e c k space y o u r space q u e s t i o n.  open parentheses 2 close parentheses C o n s i d e r space t h e space g i v e n space e q u a t i o n comma open parentheses a minus b close parentheses x squared plus open parentheses b minus c close parentheses x plus open parentheses c minus a close parentheses equals 0 G i v e n space t h a t space t h e space r o o t s space o f space t h e space e q u a t i o n space a r e space e q u a l. T h u s comma open parentheses b minus c close parentheses squared minus 4 open parentheses a minus b close parentheses open parentheses c minus a close parentheses equals 0 rightwards double arrow b squared plus c squared minus 2 b c minus 4 open parentheses a c minus a squared minus b c plus a b close parentheses equals 0 rightwards double arrow b squared plus c squared minus 2 b c minus 4 a c plus 4 a squared plus 4 b c minus 4 a b equals 0 rightwards double arrow b squared plus c squared plus 2 b c minus 4 a c plus 4 a squared minus 4 a b equals 0 rightwards double arrow b squared plus c squared plus 4 a squared plus 2 b c minus 4 a c minus 4 a b equals 0 rightwards double arrow open parentheses b plus c minus 2 a close parentheses squared equals 0 rightwards double arrow b plus c minus 2 a equals 0 rightwards double arrow b plus c equals 2 a
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