# If x, y, z are all positive real numbers. Prove that (x+ y + z)(1/x + 1/y + 1/z) ≥ 9

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If x, y, z are all positive real numbers. Prove that (x + y + z) $\big(\frac1x+\frac1y+\frac1z\big)$≥ 9

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We apply the AM, GM inequality here