If $a + b = 10$ and $ab = 21$, find the value of $a^3 + b^3$.

Given:

$a + b = 10$ and $ab = 21$

To do:

We have to find the value of $a^3 + b^3$.

Solution:

We know that,

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

Therefore,

$a + b = 10$

Cubing both sides, we get,

$(a + b)^3 = (10)^3$

$a^3 + b^3 + 3ab (a + b) = 1000$

$a^3 + b^3 + 3 \times 21 \times 10 = 1000$

$a^3 + b^3 + 630 = 1000$

$a^3 + b^3 = 1000 - 630$

$a^3 + b^3 = 370$

Hence, the value of $a^3 + b^3$ is 370.

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Updated on: 10-Oct-2022

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