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

Given:

$2x + 3y = 8$ and $xy = 2$

To do:

We have to find the value of $4x^2 + 9y^2$.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$2x + 3y = 8$

Squaring both sides, we get,

$(2x + 3y)^2 = (8)^2$

$(2x)^2 + (3y)^2 + 2 \times 2x \times 3y = 64$

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

$4x^2 + 9y^2 =64-12(2)$

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

$4x^2 + 9y^2 = 40$

The value of $4x^2+9y^2$ is $40$. 

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Updated on: 10-Oct-2022

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