If( 11a^2+13b^2)/(11c^2+13d^2) = (11a^2-13b^2)/(11c^2-13d^2),prove that a,b,c and d are proportional. 

Asked by nitinkumarsingh.singh.75 | 5th Aug, 2015, 01:10: PM

Expert Answer:

G i v e n space t h a t fraction numerator 11 a squared plus 13 b squared over denominator 11 c squared plus 13 d squared end fraction equals fraction numerator 11 a squared minus 13 b squared over denominator 11 c squared minus 13 d squared end fraction R e w r i t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma fraction numerator 11 a squared plus 13 b squared over denominator 11 a squared minus 13 b squared end fraction equals fraction numerator 11 c squared plus 13 d squared over denominator 11 c squared minus 13 d squared end fraction A p p l y i n g space c o m p o n e n d o space d i v i d e n d o comma space w e space h a v e comma fraction numerator 11 a squared plus 13 b squared plus 11 a squared minus 13 b squared over denominator 11 a squared plus 13 b squared minus 11 a squared plus 13 b squared end fraction equals fraction numerator 11 c squared plus 13 d squared plus 11 c squared minus 13 d squared over denominator 11 c squared plus 13 d squared minus 11 c squared plus 13 d squared end fraction rightwards double arrow fraction numerator 2 cross times 11 a squared over denominator 2 cross times 13 b squared end fraction equals fraction numerator 2 cross times 11 c squared over denominator 2 cross times 13 d squared end fraction rightwards double arrow a squared over b squared equals c squared over d squared T a k i n g space t h e space s q u a r e space r o o t space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma a over b equals c over d T h u s comma space a comma b comma c space a n d space d space a r e space i n space p r o p o r t i o n.

Answered by Vimala Ramamurthy | 5th Aug, 2015, 06:26: PM

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