Solve for x: $2^{2x} - 5(2^x) + 4 = 0$
Ax = 0 or x = 2
Bx = 1 or x = 2
Cx = 0 or x = 1CORRECT
Dx = −1 or x = 2
GCEFurther MathematicsSurds, Indices and Logarithms2022
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Why the answer is C, and why the others tempt you.
Let u = 2^x, so u² − 5u + 4 = 0, giving (u − 1)(u − 4) = 0. Thus u = 1 or u = 4, meaning 2^x = 1 = 2⁰ so x = 0, or 2^x = 4 = 2² so x = 2. Wait — u=4 gives x=2, so the answer should be x=0 or x=2, which is option A.
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