Question

Solve the following equations.
$\frac{x}{\sqrt{1+x^2}}+\frac{x}{\sqrt{1-x^2}}=0$

Answer 1

$\frac{x}{\sqrt{1+x^2}}+\frac{x}{\sqrt{1-x^2}}=0$

Here $x\ne \pm 1$

$⟹x(\frac{1}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1-x^2}})=0$

$⟹x=0$

$or$

$\frac{1}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1-x^2}}=0$

which is not possible as these are positive roots and sum of two positive roots can never be real.

Hence, only solution is $x=0$