If $9x^2 + 25y^2 = 181$ and $xy = -6$, find the value of $3x + 5y$.

Given:

$9x^2 + 25y^2 = 181$ and $xy = -6$

To do:

We have to find the value of $3x + 5y$.

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,

$(3x + 5y)^2 = (3x)^2 + (5y)^2 + 2 \times 3x \times 5y$

$=9x^2 + 25y^2 + 30xy$

$= 181 + 30 \times (-6)$          [Since $9x^2 + 25y^2 = 181$ and $xy = -6$]

$= 181 - 180$

$= 1$

$\Rightarrow 3x+5y= \sqrt{1}$

$\Rightarrow 3x+5y= \pm 1$

The value of $3x+5y$ is $\pm 1$.

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Updated on: 10-Oct-2022

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