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Question

If x2yza=y2zxb=z2xyc, show that (x+y+z)(a+b+c)=ax+by+cz.

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Solution

x2yza=y2zxb=z2xyc
=x2yz+y2zx+z2xya+b+c
=x(x2yz)+y(y2zx)+z(z2xy)ax+by+cz
=x3+y3+z33xyzax+by+cz
=(x+y+z)(x2+y2+z2xyyzzx)ax+by+cz
(x+y+z)(a+b+c)=ax+by+cz, by (2) and (3).

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