Question

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

Answer 1

ax = by = cz = k

`x = k/a, y = k/b, z = k/c`

L.H.S.

= `(yz)/x^2 + (zx)/y^2 + (xy)/z^2`

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

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

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

= R.H.S.