Question

if $\frac{a}{b}$+$\frac{b}{a}$= -1, then a³+b³ = ?

Answer 1

a^2 +b^2 =-ab

now,

a^3 +b^3 =(a+b)(a^2 +b^2 -ab)

=(a+b)(-ab-ab) = -2ab(a+b)