solvefor x,4x^2-4mx+5m=0

解

x, 4 x^{2} - 4 m x + 5 m = 0

x = \frac{m + m ( m - 5 )}{2}, x = \frac{m - m ( m - 5 )}{2}

解答ステップ

4 x^{2} - 4 m x + 5 m = 0

解くとthe二次式

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

簡素化

(- 4 m)^{2} - 4 \cdot 4 \cdot 5 m : 4 m (m - 5)

x_{1, 2} = \frac{- ( - 4 m ) \pm 4 m ( m - 5 )}{2 \cdot 4}

解を分離する

x_{1} = \frac{- ( - 4 m ) + 4 m ( m - 5 )}{2 \cdot 4}, x_{2} = \frac{- ( - 4 m ) - 4 m ( m - 5 )}{2 \cdot 4}

x = \frac{- ( - 4 m ) + 4 m ( m - 5 )}{2 \cdot 4} : \frac{m + m ( m - 5 )}{2}

x = \frac{- ( - 4 m ) - 4 m ( m - 5 )}{2 \cdot 4} : \frac{m - m ( m - 5 )}{2}

二次equationの解:

x = \frac{m + m ( m - 5 )}{2}, x = \frac{m - m ( m - 5 )}{2}