Ars Mathematica: Solución al problema 78

\frac{m}{k}, m, k m

\frac{m}{k} \cdot m \cdot k m = 0.125 \Rightarrow m^{3} = 0.125 \Rightarrow m = \frac{5}{10} = \frac{1}{2}

\frac{1}{2 k}, \frac{1}{2}, \frac{k}{2}

\frac{1}{2 k} + \frac{1}{2} + \frac{k}{2} = - a \Rightarrow \frac{1 + k + k^{2}}{2 k} = - a \Rightarrow 1 + k + k^{2} = - 2 a k

\frac{1}{2 k} \cdot \frac{1}{2} + \frac{1}{2 k} \cdot \frac{k}{2} + \frac{1}{2} \cdot \frac{k}{2} = b \Rightarrow 1 + k + k^{2} = 4 b k

- 2 a k = 4 b k \Rightarrow 2 b = - a

1 + k + k^{2} = - 2 a k \Rightarrow k^{2} + k (2 a + 1) + 1 = 0 \Rightarrow k = \frac{- 2 a - 1 \pm \sqrt{(2 a + 1)^{2} - 4}}{2}

x^{2} + (- 2 b + 0.5) x + 0.25 = 0 = \Rightarrow x = \frac{2 b - 0.5 \pm \sqrt{(- 2 b + 0.5)^{2} - 1}}{2}

Ars Mathematica