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If P e^x = Q e^(-x) for all real values of x, which one of the following statements is true?

1. P = Q = 0
2. P = Q = 1
3. P = 1; Q = -1
4. P / Q = 0

Correct answer: P = Q = 0

Solution

The equation P e^x = Q e^(-x) must hold for all real x, which implies that both sides must equal zero for the equality to be true at all points, leading to the conclusion that P and Q must both be zero.

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