solvefor x,x^2-8x+41=0

解

x, x^{2} - 8 x + 41 = 0

x = 4 + 5 i, x = 4 - 5 i

解答ステップ

x^{2} - 8 x + 41 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot 41}{2 \cdot 1}

簡素化

(- 8)^{2} - 4 \cdot 1 \cdot 41 : 10 i

x_{1, 2} = \frac{- ( - 8 ) \pm 10 i}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - 8 ) + 10 i}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 10 i}{2 \cdot 1}

x = \frac{- ( - 8 ) + 10 i}{2 \cdot 1} : 4 + 5 i

x = \frac{- ( - 8 ) - 10 i}{2 \cdot 1} : 4 - 5 i

二次equationの解:

x = 4 + 5 i, x = 4 - 5 i