ICSE Class 9 Answered

Asked by BHAVANA BHAT | 11 Jul, 2014, 05:25: PM

Expert Answer

$left parenthesis i i right parenthesis C o n s i d e r space t h e space g i v e n space s y s t e m space o f space s y s t e m space o f space e q u a t i o n s. x over a minus y over b equals 0.... left parenthesis 1 right parenthesis a x plus b y equals a squared plus b squared.... left parenthesis 2 right parenthesis F r o m space e q u a t i o n space left parenthesis 1 right parenthesis space w e space h a v e comma space x over a minus y over b equals 0 rightwards double arrow x over a equals y over b rightwards double arrow x equals a over b y... left parenthesis 3 right parenthesis S u b s t i t u t i n g space t h e space v a l u e space o f space x space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma a open parentheses a over b y close parentheses plus b y equals a squared plus b squared rightwards double arrow fraction numerator a squared y plus b squared y over denominator b end fraction equals a squared plus b squared rightwards double arrow open parentheses fraction numerator a squared plus b squared over denominator b end fraction close parentheses y equals a squared plus b squared rightwards double arrow y equals b S u b s t i t u t i n g space t h e space v a l u e space o f space y space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e x equals a over b cross times b rightwards double arrow x equals a left parenthesis i i i right parenthesis C o n s i d e r space t h e space g i v e n space s y s t e m space o f space e q u a t i o n s : a over x minus b over y equals 0... left parenthesis 1 right parenthesis fraction numerator a b squared over denominator x end fraction plus fraction numerator a squared b over denominator y end fraction equals a squared plus b squared.... left parenthesis 2 right parenthesis N o w space s u b s t i t u t i n g space 1 over x equals u space a n d space 1 over y equals v comma space i n space t h e space a b o v e space t w o space e q u a t i o n s comma space w e space a u minus b v equals 0... left parenthesis 3 right parenthesis a b squared u plus a squared b v equals a squared plus b squared... left parenthesis 4 right parenthesis N o w space o u r space a i m space i s space t o space s o l v e space t h e space s y s t e m space o f space e q u a t i o n s space left parenthesis 3 right parenthesis space a n d space left parenthesis 4 right parenthesis space f i r s t. M u l t i p l y space t h e space e q u a t i o n space left parenthesis 3 right parenthesis space b y space t h e space t e r m space a squared comma space w e space h a v e comma a cubed u minus a squared b v equals 0.... left parenthesis 5 right parenthesis a b squared u plus a squared b v equals a squared plus b squared... left parenthesis 4 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis comma space w e space h a v e a cubed u plus a b squared u equals a squared plus b squared rightwards double arrow a open parentheses a squared plus b squared close parentheses u equals a squared plus b squared rightwards double arrow a u equals 1 rightwards double arrow u equals 1 over a rightwards double arrow x equals a N o w space s u b s t i t u t i n g space t h e space v a l u e space o f space u space i n space e q u a t i o n space left parenthesis 5 right parenthesis space w e space h a v a cubed open parentheses 1 over a close parentheses minus a squared b v equals 0 rightwards double arrow a squared minus a squared b v equals 0 rightwards double arrow a squared open parentheses 1 minus b v close parentheses equals 0 rightwards double arrow open parentheses 1 minus b v close parentheses equals 0 rightwards double arrow v equals 1 over b rightwards double arrow y equals b T h u s space t h e space s o l u t i o n space i s space open parentheses a comma b close parentheses P l e a s e space c h e c k space h t e space q u e s t i o n space 1 left parenthesis i right parenthesis.$