If \(a^3 + b^3 = 35\) and \(ab = 6\), find the value of \(a + b\).
5
Use the identity \(a^3 + b^3 = (a+b)^3 - 3ab(a+b)\).
Let \(s = a+b\). Then:
\(s^3 - 3 \cdot 6 \cdot s = 35 \;\Rightarrow\; s^3 - 18s - 35 = 0\).
Try \(s = 5\): \(125 - 90 - 35 = 0\) ✓.
Hence \(a + b = 5\).
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