If-x-y-z-a-b-c-then-show-that-a-b-c-x-y-z-3-abc-xyz-

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 AST 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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