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-

Tinku Tara October 17, 2024 Algebra 0 Comments

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

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) .

$$\mathrm{If}\:\frac{{x}^{\mathrm{2}} \:−\:{yz}}{{a}^{\mathrm{2}} \:−\:{bc}}\:=\:\frac{{y}^{\mathrm{2}} \:−\:{zx}}{{b}^{\mathrm{2}} \:−\:{ca}}\:=\:\frac{{z}^{\mathrm{2}} \:−\:{xy}}{{c}^{\mathrm{2}} \:−\:{ab}}\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}}{{a}}\:=\:\frac{{y}}{{b}}\:=\:\frac{{z}}{{c}}\:. \\ $$

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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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