Question

The sum of all possible values of $x$ satisfying the equation $2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0$, is

• A. $\frac{5}{2}$
• B. $\frac{1}{2}$
• C. 3
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{1}{2}$

Answer 2

Given That,
$2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0$
$⇒ (2^{2x^2})^2-2^{2x^2}.2^{x+15}.2^1+(2^{x+15})^2=0$
$⇒ (2^{2x^2}-2^{x+15})^2=0$
$⇒ 2^{2x^2}-2^{x+15}=0$
$⇒ 2^{2x^2}=2^{x+15}$
$⇒ 2x^2=x+15$
$⇒ 2x^2-x-15=0$
$⇒ (2x+5)(x-3)=0$
$⇒ x=-\frac 52, \ 3$
Now, the of possible values = $-\frac 52+3 = \frac 12$

So, the correct option is (B): $\frac 12$