(m+1)x^2-(m+8)x+10=0

解

(m + 1) x^{2} - (m + 8) x + 10 = 0

x = \frac{m + 8 + m ^{2} - 24 m + 24}{2 ( m + 1 )}, x = \frac{m + 8 - m ^{2} - 24 m + 24}{2 ( m + 1 )}; m \neq = - 1

解答ステップ

(m + 1) x^{2} - (m + 8) x + 10 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - m - 8 ) \pm ( - m - 8 ) ^{2} - 4 ( m + 1 ) \cdot 10}{2 ( m + 1 )}

簡素化

(- m - 8)^{2} - 4 (m + 1) \cdot 10 : m^{2} - 24 m + 24

x_{1, 2} = \frac{- ( - m - 8 ) \pm m ^{2} - 24 m + 24}{2 ( m + 1 )}; m \neq = - 1

解を分離する

x_{1} = \frac{- ( - m - 8 ) + m ^{2} - 24 m + 24}{2 ( m + 1 )}, x_{2} = \frac{- ( - m - 8 ) - m ^{2} - 24 m + 24}{2 ( m + 1 )}

x = \frac{- ( - m - 8 ) + m ^{2} - 24 m + 24}{2 ( m + 1 )} : \frac{m + 8 + m ^{2} - 24 m + 24}{2 ( m + 1 )}

x = \frac{- ( - m - 8 ) - m ^{2} - 24 m + 24}{2 ( m + 1 )} : \frac{m + 8 - m ^{2} - 24 m + 24}{2 ( m + 1 )}

二次equationの解:

x = \frac{m + 8 + m ^{2} - 24 m + 24}{2 ( m + 1 )}, x = \frac{m + 8 - m ^{2} - 24 m + 24}{2 ( m + 1 )}; m \neq = - 1