Question:
Write the correct alternative in the following:
If $y^{1 / n}+y^{-1 / n}=2 x$, then $\left(x^{2}-1\right) y_{2}+x y_{1}=$
A. $-n^{2} y$
B. $n^{2} y$
C. 0
D. none of these
Solution:
Given:
$\mathrm{y}^{1 / \mathrm{n}}+\mathrm{y}^{-1 / \mathrm{n}}=2 \mathrm{x}$
$\frac{1}{n} y^{\frac{1}{n}-1} \frac{d y}{d x}+\frac{-1}{n} y^{\frac{-1}{n}-1} \frac{d y}{d x}=2$
$\frac{1}{n} \frac{d y}{d x}\left\{y^{\frac{1}{n}-1}-y^{\frac{-1}{n}-1}\right\}=2$