if-x-y-3a-b-y-z-3b-c-z-x-3c-a-then-prove-that-x-y-z-a-b-c-ax-by-cz-a-2-b-2-c-2-

Tinku Tara June 3, 2023 Arithmetic 0 Comments

Question Number 136640 by jahar last updated on 24/Mar/21

if ((x+y)/(3a−b))= ((y+z)/(3b−c))=((z+x)/(3c−a)) then prove that ,((x+y+z)/(a+b+c)) = ((ax+by+cz)/(a^2 +b^2 +c^2 ))

$${if}\:\frac{{x}+{y}}{\mathrm{3}{a}−{b}}=\:\frac{{y}+{z}}{\mathrm{3}{b}−{c}}=\frac{{z}+{x}}{\mathrm{3}{c}−{a}}\:{then}\: \\ $$$${prove}\:{that}\:,\frac{{x}+{y}+{z}}{{a}+{b}+{c}}\:=\:\:\:\frac{{ax}+{by}+{cz}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} } \\ $$

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