Question

If x+y = 12 and xy = 32 find the value of xsquare + y square

Answer 1

Answer:

${ \large{ \underline{ \sf{Given}}}}$

$\: \: \: \: \: \: { \sf{❍ \: x + y = 12}} \\ \\ \: \: \: \: \: \: \: \sf { ❍ \: xy \: = 32}$

${ \large{ \underline{ \sf{Find}}}}$

$\: \: \: \: \: \: { \sf{❍ \: {x}^{2} + {y}^{2} = ???}} \:$

${ \large{ \underline{ \sf{Solution}}}}$

${ \dashrightarrow{ \sf{From \: Question, x + y = 12}}}$

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By doing Squaring on both sides

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${\dashrightarrow{\sf{ {(x + y)}^{2} = {(12)}^{2} }}}$

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${\dashrightarrow{\sf{ {x}^{2} + {y}^{2} + 2xy = 144 }}}$

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From question, xy = 32

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${\dashrightarrow{\sf{ {x}^{2} + {y}^{2} + 2(32) = 144 }}}$

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${\dashrightarrow{\sf{ {x}^{2} + {y}^{2} + 64 = 144 }}}$

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${\dashrightarrow{\sf{ {x}^{2} + {y}^{2} = 144 - 64 }}}$

$\:$

${\dashrightarrow{\sf{ {x}^{2} + {y}^{2} = 80}}}$

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \sf{ \boxed{ \boxed{ \therefore{ \sf \pink{ {x}^{2} + {y}^{2} = 80 }}}}}}$