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

∴ x = `k/a, y = k/b, z = k/c`

L.H.S. = `x^2/"yz" + y^2/"zx" + z^2/"xy"`

= `(k^2/a^2)/(k/b.k/c) + (k^2/b^2)/(k/c.k/a) + (k^2/c^2)/(k/a.k/b)`

= `(k^2/a^2)/(k^2/"bc") + (k^2/b^2)/(k^2/"ca") + (k^2/c^2)/(k^2/"ab")`

= `k^2/a^2 xx "bc"/k^2 + k^2/b^2 xx "ca"/k^2 + k^2/c^2 xx "ab"/k^2`

= `"bc"/a^2 + "ca"/b^2 + "ab"/c^2`
= R.H.S.