CAT 2023 Slot 2 QA Question 2: The sum of all possible values of $x$ satisfying the equation $2^{4x^{2}} - 2^{2x^{2} + x + 16} + 2^{2x + 30} = 0$, is

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

Accepted Answer

Let us rewrite the expression so that it becomes a perfect square.

$2^{4x^{2}} - 2^{2x^{2} + x + 16} + 2^{2x + 30} = 0$
$(2^{2x^{2}})^{2} - 2^{2x^{2}} 	imes 2^{x + 16} + \dfrac{(2^{x + 16})^{2}}{4} = 0$
$(2^{2x^{2}} - \dfrac{2^{x + 16}}{2})^{2} = 0$

So, the expression inside the square must be 0.

The sum of all possible values of xxx satisfying the equation 24x2−22x2+x+16+22x+30=02^{4x^{2}} - 2^{2x^{2} + x + 16} + 2^{2x + 30} = 024x2−22x2+x+16+22x+30=0, is

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