Math, asked by haritech05, 1 year ago

if 2x-3y=8 and xy = 2, find the value 4x^2 + 9y^2

Answers

Answered by Anonymous
8
 \huge \purple {heya \: dear!!!}

Here is your answer ⤵⤵⤵⤵

 \boxed{2x - 3y = 8 \:}

 {squaring \: on \: both \: sides}

{ \purple { \bold{ {=(2x - 3y)}^{2}}}}

{ \purple{ {=(2x)}^{2} + {(3y)}^{2} - (2 \times 2x \times 3y)}}

{ \purple{ {=(4x}^{2} + {9y}^{2} - 12xy)}}

{ \boxed{(put \: value \: of \: xy)}}

{ \purple{ {=>(4x}^{2} + {9y}^{2} - 24 = 0)}}

Now,

{\purple{ {=>(4x}^{2} + {9y}^{2} = 24)}}

So,

 \purple{ \bold{ \boxed{24 \: is \: your \: answer}}}

Pls mark my answer as brainliest ✨

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Answered by Mercidez
4
\large{\boxed{\boxed{\boxed{\bold{\green{Solution : \longrightarrow}}}}}}

\bold{2x - 3y = 8}

\bold\red{On \: \: squaring \: \: both \: \: sides}

\bold\blue{ = > {(2x + 3y)}^{2} - 2.2x.3y = {(8)}^{2}} \\ \\ \bold\blue{= > 4x {}^{2} + 9y {}^{2} - 12xy= 64} \\ \\ \bold\blue{= > 4x {}^{2} + 9y {}^{2} = 64 + 12xy}

\bold{Given :} \\
\bold\red{xy = 2}

\bold{ = > {4x}^{2} + {9y}^{2} = 64 + 12(2) }\\ \\ \bold{= > {4x}^{2} + {9y}^{2} = 64 + 24} \\ \\ \bold{= > {4x}^{2} + {9y}^{2} = 88}

\bold\purple{Therefore, \: \: the \: \: value \: \: of \: \: {4x}^{2} +}\\\bold\purple{ {9y}^{2} }\bold\purple{is \: \: 88.}
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