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Question Number 144684 by mnjuly1970 last updated on 27/Jun/21


	Answered by mindispower last updated on 27/Jun/21

	$M := x y z - (x y + y z + z x) + x + y + z - 1$ $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1 x y z = x y + y z + z x$ $M = x + y + z - 1$ $h a r m o n i c a r i t h m e t i c m e a n$ $\frac{x + y + z}{3} ⩾ \frac{3}{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} = \frac{3}{1} = 3$ $\Rightarrow x + y + z ⩾ 9 \Leftrightarrow x + y + z - 1 = M = 8$ $e q u a l i t y x = y = z = 3$ $(3 - 1) (3 - 1) (3 - 1) = 8$
	Commented by mnjuly1970 last updated on 27/Jun/21

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