Question
If $a + b = 5$ and $ab = 2$, find $a^3+ b^3$.
✓
Answer
Using $(a + b)^2 = a^2 + 2ab + b^2$
$a^2+ b^2 = (a + b)^2- 2ab$
$\Rightarrow a^2 + b^2 = (5)^2 - 2(2)$
$\Rightarrow a^2 + b^2 = 25 - 4$
$\Rightarrow a^2 + b^2= 21$
$a^3 + b^3$
$= (a + b) (a^2 + b^2 - ab)$
$= (5) (21 - 2)$
$= (5) (19)$
$= 95.$
$a^2+ b^2 = (a + b)^2- 2ab$
$\Rightarrow a^2 + b^2 = (5)^2 - 2(2)$
$\Rightarrow a^2 + b^2 = 25 - 4$
$\Rightarrow a^2 + b^2= 21$
$a^3 + b^3$
$= (a + b) (a^2 + b^2 - ab)$
$= (5) (21 - 2)$
$= (5) (19)$
$= 95.$
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