Question :

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

Solution :

To understand the Question Better You can Refer to the NCERT Books and Read Chapter 9 of Maths Algebraic Expression and Identities

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