If a 3+ b 3= 72 and ab = 8, then what is the value of a + b?
6
Use the identity \(a^3+b^3=(a+b)^3-3ab(a+b)\). Let \(s=a+b\):
\[72=s^3-3(8)s=s^3-24s\]
So \(s^3-24s-72=0\). Test \(s=6\): \(216-144-72=0\). ✓
Therefore \(a+b=\mathbf{6}\).
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