Question

If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.

Answer 1

Let ax = by = cz = k, then `x = k/a, y = k/b and z = k/c`
L.H.S. = `x^2/(yz) + y^2/(zx) + z^2/(xy)`
= `k^2/(a^2 xx k/b xx k/c) + k^2/(b^2 xx k/c xx k/a) + k^2/(c^2 xx k/a xx k/b)`
= `(bc)/a^2 + (ca)/b^2 + (ab)/c^2`
= R.H.S.
Hence proved.