Math Tripos

If x, y, z are unequal, and if

$2d - 3y = \frac{(z - x)^2}{y} $

solution

The answer follows because

$\left( \frac{z}{y} \right)^2 = 1 + \frac{1}{2} + \frac{3}{2} + 1 + \ ... $

$x + y + z = \alpha$

$x = \frac{\alpha}{3}$

$y = 3x$

$z = 3\alpha + 5 + 2$