If $2x+3y=11$ and $xy=3$, find the value of $4x^2+9y^2$.

Academic Mathematics NCERT Class 8

Given:

$2x+3y=11$ and $xy=3$.
To do:
We have to find the value of $4x^2+9y^2$.

Solution:

We know that,

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

$2x+3y=11$

Squaring on both sides, we get,

$(2x+3y)^2=(11)^2$

$4x^2+9y^2+2(2x)(3y)=121$

$4x^2+9y^2+12xy=121$

$4x^2+9y^2=121-12xy$

$4x^2+9y^2=121-12(3)$ (Given $xy=3$)

$4x^2+9y^2=121-36$

$4x^2+9y^2=85$.

The value of $4x^2+9y^2$ is $85$.

Simply Easy Learning

Updated on: 10-Oct-2022

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