x^2-sqrt(2)x-1=0

解

x^{2} - 2 x - 1 = 0

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}

十進法表記

x = 1.93185 \dots, x = - 0.51763 \dots

解答ステップ

x^{2} - 2 x - 1 = 0

解くとthe二次式

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

(- 2)^{2} - 4 \cdot 1 \cdot (- 1) = 6

x_{1, 2} = \frac{- ( - 2 ) \pm 6}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - 2 ) + 6}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 6}{2 \cdot 1}

x = \frac{- ( - 2 ) + 6}{2 \cdot 1} : \frac{2 + 6}{2}

x = \frac{- ( - 2 ) - 6}{2 \cdot 1} : \frac{2 - 6}{2}

二次equationの解:

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}