If ((x^2 − yz)/(a^2 − bc)) = ((y^2 − zx)/(b^2 − ca)) = ((z^2 − xy)/(c^2 − ab)) then prove that (x/a) = (y/b) = (z/c) .


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Question Number 212576 by MATHEMATICSAM last updated on 17/Oct/24

$If \frac{x^{2} - y z}{a^{2} - b c} = \frac{y^{2} - z x}{b^{2} - c a} = \frac{z^{2} - x y}{c^{2} - a b} then$ $prove that \frac{x}{a} = \frac{y}{b} = \frac{z}{c} .$
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