Numerical answer
Find the positive value of x satisfying 2^(x+1) + 2^(2−x) = 9.
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Answer: 2
Let y = 2ˣ. Then 2^(x+1) = 2y and 2^(2−x) = 4/y. The equation becomes 2y + 4/y = 9, i.e., 2y² − 9y + 4 = 0. Factoring: (2y − 1)(y − 4) = 0, so y = 4 or y = 1/2. y = 4 gives x = 2; y = 1/2 gives x = −1. The positive value is x = 2.
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