If $2x + 3y = 13$ and $xy = 6$, find the value of $8x^3 + 21y^3$.

Given:

$2x + 3y = 13$ and $xy = 6$

To do:

We have to find the value of $8x^3 + 21y^3$.

Solution:

We know that,

$(a+b)^3=a^3 + b^3 + 3ab(a+b)$

Therefore,

$2x + 3y = 13$

Cubing both sides, we get,

$(2x + 3y)^3 = (13)^3$

$(2x)^3 + (3y)^3 + 3 \times 2x \times 3y(2x + 3y) = 2197$

$8x^3 + 27y^3 + 18xy(2x + 3y) = 2197$

$8x^3 + 27y^3 + 18 \times 6 \times 13 = 2197$

$8x^3 + 27y^3 + 1404 = 2197$

$8x^3 + 27y^3 = 2197 - 1404$

$8x^3 + 27y^3 = 793$

The value of \( 8x^{3}+27y^3 \) is $793$.  

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Updated on: 10-Oct-2022

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