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

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Last updated date: 15th Jul 2024
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Answer
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We have,
\[{\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy\]
\[ \Rightarrow \,\,{12^{2\,}} = {x^2} + {y^2} + 2 \times 32\]
\[ \Rightarrow \,\,144 = {x^2} + {y^2} + 64\]
\[ \Rightarrow 144 - 64 = {x^2} + {y^2}\]
\[ \Rightarrow {x^2} + {y^2} = 80\]