If x = 2 + 2^{1/2} + 2^{3/2}, then what is x^2 - 4x - 10 equal to?

Explanation

We can rewrite the equation as x - 2 = \sqrt{2} + 2\sqrt{2} = 3\sqrt{2}. Squaring both sides yields (x - 2)^2 = (3\sqrt{2})^2, which gives x^2 - 4x + 4 = 18. Thus, x^2 - 4x - 14 = 0, meaning x^2 - 4x - 10 = 4.

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