VTMO 2026 - Grade 8 - Semifinal - SET 1 - Self-study Question 20

Let $a,b$ be the two distinct real roots of $P(x)=x^2-10x+2$. Given $a+b=10$, $ab=2$, evaluate $A=\dfrac1{a^3+2a}+\dfrac1{b^3+2b}$.