Question
If $m - n = -2$ and $m^3 - n^3 = -26$, find $mn$.
✓
Answer
$m - n = -2, m^3 - n^3 = -26$
$(m - n)^3 = m^3 - n^3 - 3mn (m - n)$
$\Rightarrow (-2)^3 = -26 - 3mn (-2)$
$\Rightarrow 6mn$
$= - 8 + 26$
$= 18$
$\Rightarrow mn = 3.$
$(m - n)^3 = m^3 - n^3 - 3mn (m - n)$
$\Rightarrow (-2)^3 = -26 - 3mn (-2)$
$\Rightarrow 6mn$
$= - 8 + 26$
$= 18$
$\Rightarrow mn = 3.$
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