sqrt(2)x^2-3x-5=0

解

2 x^{2} - 3 x - 5 = 0

x = \frac{3 + 9 + 20 2}{2 2}, x = \frac{3 - 9 + 20 2}{2 2}

十進法表記

x = 3.21948 \dots, x = - 1.09816 \dots

解答ステップ

2 x^{2} - 3 x - 5 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 2 ( - 5 )}{2 2}

(- 3)^{2} - 42 (- 5) = 9 + 202

x_{1, 2} = \frac{- ( - 3 ) \pm 9 + 20 2}{2 2}

解を分離する

x_{1} = \frac{- ( - 3 ) + 9 + 20 2}{2 2}, x_{2} = \frac{- ( - 3 ) - 9 + 20 2}{2 2}

x = \frac{- ( - 3 ) + 9 + 20 2}{2 2} : \frac{3 + 9 + 20 2}{2 2}

x = \frac{- ( - 3 ) - 9 + 20 2}{2 2} : \frac{3 - 9 + 20 2}{2 2}

二次equationの解:

x = \frac{3 + 9 + 20 2}{2 2}, x = \frac{3 - 9 + 20 2}{2 2}