Question

If \[x + y = 12\]and\[xy = 32\], find the value of \[{x^2} + {y^2}\].

Answer 1

We have,
\[{\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy\]
\[ \Rightarrow \,\,{12^{2\,}} = {x^2} + {y^2} + 2 \times 32\]
\[ \Rightarrow \,\,144 = {x^2} + {y^2} + 64\]
\[ \Rightarrow 144 - 64 = {x^2} + {y^2}\]
\[ \Rightarrow {x^2} + {y^2} = 80\]