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Question: Answered & Verified by Expert
If $x^2+y^2=t-\frac{1}{t}, x^4+y^4=t^2+\frac{1}{t^2}$, then $x^3 y \frac{d y}{d x}=$
MathematicsDifferentiationJEE Main
Options:
  • A 1
  • B 2
  • C 3
  • D 4
Solution:
1543 Upvotes Verified Answer
The correct answer is: 1
$\begin{aligned} & x^4+y^4=\left(t-\frac{1}{t}\right)^2+2=\left(x^2+y^2\right)^2+2 \\ & \Rightarrow x^2 y^2=-1 \Rightarrow y^2=-\frac{1}{x^2}\end{aligned}$
Differentiating, we get $2 y \frac{d y}{d x}=\frac{2}{x^3}$ or $x^3 y \frac{d y}{d x}=1$

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