Find the value of $27x^3 + 8y^3$ if $3x + 2y = 20$ and $xy = \frac{14}{9}$

Given:

$3x + 2y = 20$ and $xy = \frac{14}{9}$.

To do:

We have to find the value of $27x^3 + 8y^3$.

Solution:

$3 x+2 y=20$

Cubing both sides, we get,

$(3 x+2 y)^{3}=(20)^{3}$

$(3 x)^{3}+(2 y)^{3}+3 \times 3 x \times 2 y(3 x+2 y)=8000$

$27 x^{3}+8 y^{3}+3 \times 3 \times 2 x y(3 x+2 y)=8000$

$27 x^{3}+8 y^{3}+18 \times \frac{14}{9} \times 20=8000$

$27 x^{3}+8 y^{3}+560=8000$

$27 x^{3}+8 y^{3}=8000-560$

$27 x^{3}+8 y^{3}=7440$

The value of $27 x^{3}+8 y^{3}$ is $7440$. 

Tutorialspoint

Updated on: 10-Oct-2022

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