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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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