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If a, b, x, y are positive natural numbe...

If a, b, x, y are positive natural numbers such that `(1)/(x) + (1)/(y) = 1` then prove that `(a^(x))/(x) + (b^(y))/(y) ge ab`.

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To prove that \(\frac{a^x}{x} + \frac{b^y}{y} \geq ab\) given that \(\frac{1}{x} + \frac{1}{y} = 1\), we can use the method of inequalities, specifically the AM-GM inequality (Arithmetic Mean - Geometric Mean inequality). ### Step-by-Step Solution: 1. **Start with the given equation**: \[ \frac{1}{x} + \frac{1}{y} = 1 \] ...
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