m^3 + n^3 = (m + n)^3 - 3mn(m + n).
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- Y = 4\left(\frac{3}{2}\right)^2 - 12\left(\frac{3}{2}\right) + 9 = 4\left(\frac{9}{4}\right) - 18 + 9 = 9 - 18 + 9 = 0.
- Thus, the minimum yield is \(0\) at \(x = \frac{3}{2}\), and the minimum value is \(\boxed{0}\).
- Question:** If \(m + n = 7\) and \(m^2 + n^2 = 29\), find \(m^3 + n^3\).
- We are given \(m + n = 7\) and \(m^2 + n^2 = 29\).
- First, compute \(mn\) using the identity:
- Now substitute into the formula:
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