Vgln. tweede graad

Los op. Vermijd indien mogelijk het gebruik van de discriminant.

\(\frac{17}{20}x=-\frac{1}{5}x^2-\frac{1}{5}\)

\(\frac{17}{20}x=-\frac{1}{5}x^2-\frac{1}{5} \\ \Leftrightarrow \frac{1}{5}x^2+\frac{17}{20}x+\frac{1}{5}=0 \\ \Leftrightarrow \color{red}{20.} \left(\frac{1}{5}x^2+\frac{17}{20}x+\frac{1}{5}\right)=0 \color{red}{.20} \\ \Leftrightarrow 4x^2+17x+4=0 \\\text{We zoeken de oplossingen van } \color{blue}{4x^2+17x+4=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (17)^2-4.4.4 & &\\ & = 289-64 & & \\ & = 225 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-17-\sqrt225}{2.4} & & = \frac{-17+\sqrt225}{2.4} \\ & = \frac{-32}{8} & & = \frac{-2}{8} \\ & = -4 & & = \frac{-1}{4} \\ \\ V &= \Big\{ -4 ; \frac{-1}{4} \Big\} & &\end{align} \\ -----------------\)