If x- y- z are positive- then prove that x-y-z 1-x-1-y-1-z - 9

Using the relation AM. ≥ H.M. x+y+z/3≥3/1/x+1/y+1/z⇒ ( x+y+z ) ( 1/x+1/y+1/z )≥ 9 ...

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Logarithm of a Complex Number

If x, y, z ...

Question

If $x, y, z$ are positive, then prove that $(x + y + z) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z}) \geq 9$

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x, y, z

(x + y) (y + z) (z + x) (\frac{1}{x} + \frac{1}{y}) (\frac{1}{y} + \frac{1}{z}) (\frac{1}{z} + \frac{1}{x})

(1 - x) (1 - y) (1 - z) \geq k x y z

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(x + y) (y + z) (z + x) (\frac{1}{x} + \frac{1}{y}) (\frac{1}{y} + \frac{1}{z}) (\frac{1}{z} + \frac{1}{x})

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\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

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