If $a^4 + a^2 b^2 + b^4 = 8$ and $a^2 + ab + b^2 = 4$, $a^2 + b^2 = ?$

Since $a^4+a^2b^2+b^4=(a^2+ab+b^2)(a^2-ab+b^2)$, dividing by gives . Adding to this gives , so .