If \(2^{x+y} = 4^{x-y} = \sqrt{32}\), then \(xy = \) ___.
Question and options
If , then ___.
Answer and explanation
Correct answer: B - \(\frac{75}{64}\)
sqrt(32) = 2^(5/2). So x + y = 5/2 and 2(x - y) = 5/2, giving x - y = 5/4. Then x = 15/8, y = 5/8, xy = 75/64.
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