If $a + b = 5$ and $a^{2} + b^{2} = 13$, find the value of $a^{4} + b^{4}$.

Question

Aicharya · Accepted Answer

$ab = \dfrac{(a+b)^{2} - (a^{2}+b^{2})}{2} = \dfrac{25-13}{2} = 6$. $a^{4}+b^{4} = (a^{2}+b^{2})^{2} - 2(ab)^{2} = 169 - 72 = 97$.

Solution