If `x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl-m^(2))`, then prove that `lx + my + nz = 0`.

Explanation

`x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl - m^(2)) = k " (let)" [k ne 0]`
` :. x = k (lm - n^(2)), y = k (nm - l^(2)), z = k (ml - m^(2))`
or, ` lx = k (l^(2)m - n^(2)l), my = k (m^(2)n - l^(2)m), nz = k (n^(2) l - m^(2)n)`
or, `lx + my + nz = k(l^(2) m - n^(2)l + m^(2)n - l^(2)m + n^(2)l - m^(2)n)`
` = k xx 0 = 0`.
` :. lx + my + nz = 0`.