Question
If $x^3 + y^3 = 9$ and $x + y = 3$, find $xy.$
✓
Answer
$x^3 + y^3 = 9, x + y = 3$
$(x + y)^3 = x^3+ y^3+ 3xy (x + y)$
$\Rightarrow (3)^3 = 9 + 3xy (3)$
$\Rightarrow 27 = 9 + 9xy$
$\Rightarrow 9xy = 27 - 9 = 18$
$\Rightarrow xy = 2.$
$(x + y)^3 = x^3+ y^3+ 3xy (x + y)$
$\Rightarrow (3)^3 = 9 + 3xy (3)$
$\Rightarrow 27 = 9 + 9xy$
$\Rightarrow 9xy = 27 - 9 = 18$
$\Rightarrow xy = 2.$
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