Question

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

Answer 1

$\huge \purple {heya \: dear!!!}$

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,

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

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Answer 2

$\large{\boxed{\boxed{\boxed{\bold{\green{Solution : \longrightarrow}}}}}}$

$\bold{2x - 3y = 8}$

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

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

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

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

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