If $a + b - 12 = 0$ and $a b = 27$ , then find $a^{3} + b^{3}$ .

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Solution

We have,

$a + b = 12$ and $a b = 27$

We know that

$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$

Therefore,

$(12)^{3} = a^{3} + b^{3} + 3 \times 27 \times 12$

$1728 = a^{3} + b^{3} + 972$

$a^{3} + b^{3} = 1728 - 972 = 756$

Hence, this is the answer.

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