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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  (((a + b + c)/(x + y + z)))^3  = ((abc)/(xyz)) .
$$\mathrm{If}\:{x}\::\:{y}\::\:{z}\:=\:{a}\::\:{b}\::\:{c}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\frac{{a}\:+\:{b}\:+\:{c}}{{x}\:+\:{y}\:+\:{z}}\right)^{\mathrm{3}} \:=\:\frac{{abc}}{{xyz}}\:. \\ $$
Answered by AST last updated on 24/Dec/23
x=ka;y=kb;z=kc  (((a+b+c)/(x+y+z)))^3 =(1/k^3 )=((abc)/(k^3 abc))=((abc)/(xyz))
$${x}={ka};{y}={kb};{z}={kc} \\ $$$$\left(\frac{{a}+{b}+{c}}{{x}+{y}+{z}}\right)^{\mathrm{3}} =\frac{\mathrm{1}}{{k}^{\mathrm{3}} }=\frac{{abc}}{{k}^{\mathrm{3}} {abc}}=\frac{{abc}}{{xyz}} \\ $$

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