$a^2 + b^2 - \frac{ab}{2} = c^2 + d^2 + \frac{cd}{2} = 256$
$ac + bd = 240$ where a, b ,c ,d are positive reals, maximize $(ab +cd)^2$
looking at the equations and restrictions, I think Cauchy can be applied
$(a^2+c^2)(b^2+d^2)> (ab + cd)^2$ so we just need to find the value of the LHS
but I'm finding it hard to manipulate them and i cant seem to find an application for the ac+bd =240.