If $a + b = 8$ and $a b = 15$ , find $a^{3} + b^{3}$ .

122

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132

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152

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172

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Solution

The correct option is D 152
$a + b = 8$
Cubing both sides,
$(a + b)^{3} = 8^{3}$
Applying the formula,
$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$\Rightarrow$ $a^{3} + b^{3} + 3 a b (a + b) = 512$

Substituting,
$a + b = 8; a b = 15$

$a^{3} + b^{3} + 3 \times 15 \times 8 = 512$
$a^{3} + b^{3} + 360 = 512$
$a^{3} + b^{3} = 512 - 360 = 152$

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