Question

The sum of values of $x$ satisfying the equation $(31+8\sqrt{15}{)}^{x^2-3}=(32+8\sqrt{15}{)}^{x^2-3}$ is

• A. $3$
• B. $0$
• C. $2$
• D. none of these

Answer 1

Answer: (B)

$0$

$x^a=y^a$ is possible only when $x=y$ or $a=0$
Since $x=y$ is not possible
So $a=0$
$x^2-3=0\Rightarrow x=\sqrt{3}orx=-\sqrt{3}$
So sum of roots is 0