CAT 2023 Surds and Indices Question (Hard)

Question

The sum of all possible values of satisfying the equation 2 4x 2 - 2 2x 2 x 16 2 2x 30 0 is

Accepted Answer

Given equation 2 4x 2 - 2 2x 2 x 16 2 2x 30 0 --- Step 1 Let A 2 2x 2 Then the equation becomes A 2 - 2 x 16 A 2 2x 30 0 --- Step 2 Divide the entire equation by 2 2x to simplify powers 2 2x - 2 16 2 x 2 30 0 Let B 2 x 2 2x 2 - x So the equation becomes B 2 - 2 16 B 2 30 0 --- Step 3 Recognize it as

CAT 2023

Quantitative

Surds and Indices

Hard

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

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