Question : If $m+n=-2$, then the value of $m^{3}+n^{3}-6mn$ is:
Option 1: 8
Option 2: 4
Option 3: –8
Option 4: –4
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Correct Answer: –8
Solution :
Given: $m+n=-2$ and $ab=24$
We know that $(a+b)^3=a^3+b^3+3ab(a+b)$
Now, $m+n=-2$
Cubing both sides.
⇒ $-2^3=m^3+n^3+3(mn)(-2)$
⇒ $m^3+n^3-6mn=-8$
Hence, the correct answer is –8.
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