If $a + b = 8$ and $ab = 6$, find the value of $a^3 + b^3$.

Given: 

$a + b = 8$ and $ab = 6$

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,

$a + b = 8$

Cubing both sides, we get,

$(a + b)^3 = (8)^3$

$a^3 + b^3 + 3ab(a + b) = 512$

$a^3 + b^3 + 3 \times 6 \times 8 = 512$

$a^3 + b^3 + 144 = 512$

$a^3 + b^3 = 512 - 144$

$a^3 + b^3 = 368$

Hence, $a^3 + b^3 = 368$.

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Updated on: 10-Oct-2022

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