If x : y : z = a : b : c then show that (((a + b + c)/(x + y + z)))^3 = ((abc)/(xyz)) .


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Question Number 202315 by MATHEMATICSAM last updated on 24/Dec/23

$If x : y : z = a : b : c then show that$ ${(\frac{a + b + c}{x + y + z})}^{3} = \frac{a b c}{x y z} .$
	Answered by deleteduser1 last updated on 24/Dec/23

	$x = k a; y = k b; z = k c$ ${(\frac{a + b + c}{x + y + z})}^{3} = \frac{1}{k^{3}} = \frac{a b c}{k^{3} a b c} = \frac{a b c}{x y z}$
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