If (x+y)=3, x y=2, then what is the value of x³+ y³ ? · ABC26GN1225

$(x+y)=3 \Rightarrow(x+y)^{2}=9$ $$\begin{aligned} & \Rightarrow x^{2}+y^{2}+2 x y=9 \\ & \Rightarrow x^{2}+y^{2}=9-2 x y=9-4=5 . \end{aligned} \begin{aligned} \therefore x^{3}+y^{3} & =(x+y)\left(x^{2}+y^{2}-x y\right)=3(5-2) \\ & =3 \times 3=9 \cdot\left[\because x+y=3, x^{2}+y^{2}=5, x y=2\right] \end{aligned}$$