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CBSE Class 12-science Answered

if y=[log (x+rt(x2+1))^2, show that (1+x2)y2+xy1=2
Asked by lekhakarthikeyan | 05 Dec, 2018, 09:45: PM
answered-by-expert Expert Answer
I assume the question is begin mathsize 12px style y space equals space log space open parentheses x plus square root of x squared plus 1 space end root close parentheses squared end style and show that (1+x2) y2 + x y1 = 0
begin mathsize 12px style y space equals space log open parentheses x plus square root of x squared plus 1 end root close parentheses squared space equals space 2 space log open parentheses x plus square root of x squared plus 1 end root close parentheses y subscript 1 space equals space fraction numerator d y over denominator d x end fraction space equals space 2 fraction numerator 1 over denominator x plus square root of x squared plus 1 end root end fraction open parentheses 1 plus fraction numerator 2 x over denominator 2 square root of x squared plus 1 end root end fraction close parentheses space equals space fraction numerator 2 over denominator square root of x squared plus 1 end root end fraction space.............. left parenthesis 1 right parenthesis d i f f e r e n t i a t e space a g a i n comma space w e space g e t y subscript 2 space equals space fraction numerator negative 2 begin display style fraction numerator 2 x over denominator 2 square root of x squared plus 1 end root end fraction end style over denominator x squared plus 1 end fraction space space open parentheses x squared plus 1 close parentheses y subscript 2 space equals fraction numerator negative 2 x over denominator square root of x squared plus 1 end root end fraction......... left parenthesis 2 right parenthesis U sin g space e q n. left parenthesis 1 right parenthesis space i n space e q n. left parenthesis 2 right parenthesis comma space w e space g e t space left parenthesis x squared plus 1 right parenthesis y subscript 2 plus 2 y subscript 1 space equals space 0 end style
Answered by Thiyagarajan K | 06 Dec, 2018, 06:01: AM

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