If a + b = 5 and a² + b² = 17, find (a³ + b³)/ab.
65/4
Since \((a+b)^2 = a^2+b^2+2ab\), we get \(ab = \frac{(a+b)^2-(a^2+b^2)}{2} = \frac{25-17}{2} = 4\).
Using \(a^3+b^3 = (a+b)(a^2+b^2-ab)\), we get \(a^3+b^3 = 5(17-4) = 5 \times 13 = 65\).
Therefore, \(\frac{a^3+b^3}{ab} = \frac{65}{4}\).
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