If $a^{3} + b^{3} = 27$ and $a^{2} + b^{2} - a b = 9$ , then $a + b =$ ___

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Solution

We know that $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$

$\Rightarrow a + b = \frac{a^{3} + b^{3}}{a^{2} + b^{2} - a b}$

$= \frac{27}{9} = 3$

$\Rightarrow a + b = 3$

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If a3+b3=27 and a2+b2−ab=9, then a+b=___

We know that a3+b3=(a+b)(a2+b2−ab) ⇒a+b=a3+b3a2+b2−ab =279=3 ⇒a+b=3

If $a^{3} + b^{3} = 27$ and $a^{2} + b^{2} - a b = 9$ , then $a + b =$ ___

We know that $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$

$\Rightarrow a + b = \frac{a^{3} + b^{3}}{a^{2} + b^{2} - a b}$

$= \frac{27}{9} = 3$

$\Rightarrow a + b = 3$