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Solve for x: (3 + 2*sqrt(2))^(x/2) + (3 - 2*sqrt(2))^(x/2) = 34.

1. x = +-4
2. x = +-2
3. x = 4 only
4. x = +-6

Correct answer: x = +-4

Solution

The two bases multiply to 1, so put u = (3+2sqrt2)^(x/2); the equation becomes u + 1/u = 34. Solve the resulting quadratic and translate back to x.

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