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If a x^2+2 h x y+b y^2=3 , then d^2 y d x^2 =

Options

  1. A(h x^2+b y+a x ) (a x+h y)^2
  2. B(a x y+h x^2+b y x ) (a x+b y)^2
  3. C3 (h^2-a b ) (h x+b y)^3
  4. D(a b+h)^2 (a x+h y)^2 [h (x^2+y^2 )+x y(a+b) ]

Correct answer

C. 3 (h^2-a b ) (h x+b y)^3

Step-by-step solution

We have, a x^2+2 h x y+b y^2=3 On differentiating with respect to x , we get aligned & 2 a x+2 h x d y d x +2 h y+2 b y d y d x =0 & d y d x =- (a x+h y) (b y+h x) aligned Again differentiating with respect to x , we get aligned & 2 a+2 h x d^2 y d x^2 +2 h d y d x +2 h d y d x +2 b ( d y d x )^2 &+2 b y d^2 y d x^2 =0 aligned aligned & d^2 y d x^2 (h x+b y)=- (a+2 h d y d x +b ( d y d x )^2 ) & d^2 y d x^2 (h x+b y)= &- (a+2 h ( -a x-h y h x+b y )+b ( -a x-h y h x+b y )^2 ) aligned d^2 y d x^2 (h x+b y)=- [ a(h x+

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