Given:

$\displaystyle a^2+b^2=c^2+d^2$

$\displaystyle a^3+b^3=c^3+d^3$

Show that:

$\displaystyle a+b=c+d$

Obvi, factor the second equation and we get

$\displaystyle (a+b)(a^2+b^2-ab)=(c+d)(c^2+d^2-cd)$

So, we only have to show that ab=cd.

Can anyone crack it?