(5+4sqrt(7))x^2+(4-2sqrt(7))x-1=0

解

(5 + 47) x^{2} + (4 - 27) x - 1 = 0

x = \frac{6 + 7}{29}, x = - \frac{7 - 2}{3}

十進法表記

x = 0.29812 \dots, x = - 0.21525 \dots

解答ステップ

(5 + 47) x^{2} + (4 - 27) x - 1 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 4 - 2 7 ) \pm ( 4 - 2 7 ) ^{2} - 4 ( 5 + 4 7 ) ( - 1 )}{2 ( 5 + 4 7 )}

(4 - 27)^{2} - 4 (5 + 47) (- 1) = 8

x_{1, 2} = \frac{- ( 4 - 2 7 ) \pm 8}{2 ( 5 + 4 7 )}

解を分離する

x_{1} = \frac{- ( 4 - 2 7 ) + 8}{2 ( 5 + 4 7 )}, x_{2} = \frac{- ( 4 - 2 7 ) - 8}{2 ( 5 + 4 7 )}

x = \frac{- ( 4 - 2 7 ) + 8}{2 ( 5 + 4 7 )} : \frac{6 + 7}{29}

x = \frac{- ( 4 - 2 7 ) - 8}{2 ( 5 + 4 7 )} : - \frac{7 - 2}{3}

二次equationの解:

x = \frac{6 + 7}{29}, x = - \frac{7 - 2}{3}