Question

If x + y = 12 and xy = 14, find the value of (x² + y²).

Answer 1

$$\begin{gathered} x+y=12 \\ \mathrm{On}\mathrm{squaring}\mathrm{both}\mathrm{the}\mathrm{sides}: \\ \Rightarrow {\left(x+y\right)}^2={\left(12\right)}^2 \\ \Rightarrow x^2+y^2+2xy=144 \\ \Rightarrow x^2+y^2=144-2xy \\ \mathrm{Given}: \\ xy=14 \\ \Rightarrow x^2+y^2=144-2\left(14\right) \\ \Rightarrow x^2+y^2=144-28 \\ \Rightarrow x^2+y^2=116 \\ \mathrm{Therefore},\mathrm{the}\mathrm{value}\mathrm{of}{x}^2+y^2\mathrm{is}116. \end{gathered}$$