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Home » x^2 + y^2 + rac34z^2 + 2z - 4 = 0. - Baxtercollege

x^2 + y^2 + rac34z^2 + 2z - 4 = 0. - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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The vertex of a parabola \(ax^2 + bx + c\) occurs at:
x = -\frac{b}{2a} = -\frac{-12}{2 \cdot 4} = \frac{12}{8} = \frac{3}{2...
Substitute \(x = \frac{3}{2}\) into the equation to find the minimum y...
Y = 4\left(\frac{3}{2}\right)^2 - 12\left(\frac{3}{2}\right) + 9 = 4\l...
Thus, the minimum yield is \(0\) at \(x = \frac{3}{2}\), and the minim...
Question:** If \(m + n = 7\) and \(m^2 + n^2 = 29\), find \(m^3 + n^3\...
m^3 + n^3 = (m + n)^3 - 3mn(m + n).
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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