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Home / Aptitude Tests / Further Mathematics / Solve: \(4(2^{x^2}) ...

Solve: $4(2^{x^2}) = 8^{x}$ ...

Solve: $4(2^{x^2}) = 8^{x}$

A.

(1, 2)

B.

(1, -2)

C.

(-1, 2)

D.

(-1, -2)

View answer & explanation

Correct answer is A

$4(2^{x^2}) = 8^{x} \equiv (2^{2})(2^{x^2}) = (2^{3})^{x}$

$\implies 2^{2 + x^{2}} = 2^{3x}$

Comparing bases, we have

$2 + x^{2} = 3x \implies x^{2} - 3x + 2 = 0$

$x^{2} - 2x - x + 2 = 0$

$x(x - 2) - 1(x - 2) = 0$

$(x - 1) = 0$ or $(x - 2) = 0$

$x = \text{1 or 2}$

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