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If $3x + 5y = 11$ and $xy = 2$, find the value of $9x^2 + 25y^2$.
Given:
$3x + 5y = 11$ and $xy = 2$
To do:
We have to find the value of $9x^2+25y^2$.
Solution:
The given expressions are $3x + 5y = 11$ and $xy = 2$. Here, we have to find the value of $9x^2+25y^2$. So, by squaring the given expression and using the identity $(a+b)^2=a^2+2ab+b^2$, we can find the required value.
$xy = 2$............(i)
$(a+b)^2=a^2+2ab+b^2$.............(ii)
Now,
$3x + 5y = 11$
Squaring on both sides, we get,
$(3x + 5y)^2 = (11)^2$ [Using (ii)]
$(3x)^2+2(3x)(5y)+(5y)^2=121$
$9x^2+30xy+25y^2=121$
$9x^2+30(2)+25y^2=121$ [Using (i)]
$9x^2+60+25y^2=121$
$9x^2+25y^2=121-60$ (Transposing $60$ to RHS)
$9x^2+25y^2=61$
Hence, the value of $9x^2+25y^2$ is $61$.
Updated on: 01-Apr-2023
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