Cho x + y = 1. tính a = x^3 + y^3 + 3xy

* Hướng dẫn giải

Cho x + y = 1

$\begin{array}{l}\mathrm{A}={\mathrm{x}}^3+{\mathrm{y}}^3+3\mathrm{xy}=\left(\mathrm{x}+\mathrm{y}\right)\left({\mathrm{x}}^2-\mathrm{xy}+{\mathrm{y}}^2\right)+3\mathrm{xy}\\ =1.\left({\mathrm{x}}^2-\mathrm{xy}+{\mathrm{y}}^2\right)+3\mathrm{xy}={\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2={\left(\mathrm{x}+\mathrm{y}\right)}^2\end{array}$