Question

If 2x + 3y= 8 and xy =2,find the value of ${4x}^{2} {9y}^{2}}}$ ​

Answer 1

$\Large\boxed{ANSWER=40}$

$\Large\boxed{Step\:by \:step\: explaination}$

We have${2x + 3y = 8}$

=> ${(2x + 3y)}^{2} ={8}^{2}$ [On squaring both sides]

=>${(2x)}^{2}+ 2 * 2x * 3y + {3y}^{2} = 64$

=>${4x} ^{2} + 12xy + {9y}^{2}=64=>{4x}^{2} + {9y}^{2} + 12xy = 64$

=>${4x} ^{2} + {9y}^{2} + 12*2 = 64$ ${[xy = 2]}$

=>${4x}^{2} + {9y}^{2} + 24 = 64 => {4x}^{2} + {9y}^{2} = 64 - 24$

=>${4x}^{2} + {9y} ^{2} = 40$

$\Large\boxed{Thus,{4x}^{2} + {9y}^{2} = 40}}}}$

$\color{red} \huge\bold\star \underline \mathcal {SOLVED}\star$

Answer 2

2x+3y = 8

⇒(2x+3y)²=(8)²

⇒4x²+9y²+12xy = 64

⇒4X²+9Y²+12*2=64

⇒4x²+9y²=64-24

⇒4X²+9Y²=40