Question

The sum of values of $x$ satisfying the equation $(31+8\sqrt{15}{)}^{x^2-3}+1=(32+8\sqrt{15}{)}^{x^2-3}$ is

• A. $3$
• B. $2$
• C. $0$
• D. None of the above.

Answer 1

Answer: (C)

$0$

Given ${(31+8\sqrt{15})}^{x^2-3}+1={(32+8\sqrt{15})}^{x^2-3}$

Above equation satisfied only when

$x^2-3=1\because 32+8\sqrt{15}=1+31+8\sqrt{15}$

$\therefore x^2=4$

$x=\pm 2$

Sum of values of x which satisfies above equation$=-2+2$

$=0$