(x2-yz)/(a2-bc)=(y2-zx)/(b2-ca)=(z2-xy)/(c2-ab) then prove that x/a=y/b=z/c
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Let ax = by = cz = k, then
x = k/a, y = k/b and z = k/c
L.H.S. = x2/yz + y2/zx + z2/xy
= k2/a2 × k/b × k/c + k2/b2 × k/c × k/a + k2/c2 × k/a × k/b
= bc/a2 + ca/b2 + ab/c2
= R.H.S.
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