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Let r, s, and t be solutions of the equation x^3 - 4x^2 - 7x + 12 = 0. Compute
\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}

 Mar 4, 2025
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\(x^3 - 4x^2 - 7x + 12=0\\ The\ equation\ is\ solved\ with\ \color{blue}WolframAlpha.\\ \color{blue}r=-2.0912\\ \color{blue}s=1.1648\\ \color{blue}t=4.9265\)

 

\(\dfrac{rs}{t^2} + \dfrac{rt}{s^2} + \dfrac{st}{r^2}\\ =\dfrac{-2.0912\cdot 1.1648}{4.9265^2} + \dfrac{-2.0912\cdot 4.9265}{1.1648^2} + \dfrac{1.1648\cdot 4.9265}{(-2.0912)^2}\\ \color{blue}=-6.38147970131\)

 

laugh !

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 Mar 4, 2025

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