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2.4 The product of tyo numbers \( x \) and \( y \) is 60 and their sum is 15 . Show that \( \frac{1}{x}+\frac{1}{y}=\frac{1}{4} \).

Ask by Hammond Young. in South Africa
Mar 09,2025

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\[ \frac{1}{x} + \frac{1}{y} = \frac{1}{4} \]

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To prove that \( \frac{1}{x} + \frac{1}{y} = \frac{1}{4} \) given that the product \( xy = 60 \) and the sum \( x + y = 15 \), we can rewrite the sum of the reciprocals: \[ \frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy} \] Substituting the given values into the equation: \[ \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} = \frac{15}{60} \] Now simplifying \( \frac{15}{60} \): \[ \frac{15}{60} = \frac{1}{4} \] Thus, we have shown that \( \frac{1}{x} + \frac{1}{y} = \frac{1}{4} \).

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