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人気のある代数 >

mx^2-(m^2+5m-5)x+5m-9=x^2

解

m x^{2} - (m^{2} + 5 m - 5) x + 5 m - 9 = x^{2}

解

x = \frac{m ^{2} + 5 m - 5 + m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}, x = \frac{m ^{2} + 5 m - 5 - m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}; m \neq = 1

解答ステップ

m x^{2} - (m^{2} + 5 m - 5) x + 5 m - 9 = x^{2}

拡張

m x^{2} - (m^{2} + 5 m - 5) x + 5 m - 9 : m x^{2} - m^{2} x - 5 m x + 5 x + 5 m - 9

m x^{2} - m^{2} x - 5 m x + 5 x + 5 m - 9 = x^{2}

x^{2}

を左側に移動します

m x^{2} - m^{2} x - 5 m x + 5 x + 5 m - 9 - x^{2} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

(m - 1) x^{2} + (- m^{2} - 5 m + 5) x + 5 m - 9 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - m ^{2} - 5 m + 5 ) \pm ( - m ^{2} - 5 m + 5 ) ^{2} - 4 ( m - 1 ) ( 5 m - 9 )}{2 ( m - 1 )}

簡素化

(- m^{2} - 5 m + 5)^{2} - 4 (m - 1) (5 m - 9) : m^{4} + 10 m^{3} - 5 m^{2} + 6 m - 11

x_{1, 2} = \frac{- ( - m ^{2} - 5 m + 5 ) \pm m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}; m \neq = 1

解を分離する

x_{1} = \frac{- ( - m ^{2} - 5 m + 5 ) + m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}, x_{2} = \frac{- ( - m ^{2} - 5 m + 5 ) - m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}

x = \frac{- ( - m ^{2} - 5 m + 5 ) + m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )} : \frac{m ^{2} + 5 m - 5 + m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}

x = \frac{- ( - m ^{2} - 5 m + 5 ) - m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )} : \frac{m ^{2} + 5 m - 5 - m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}

二次equationの解:

x = \frac{m ^{2} + 5 m - 5 + m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}, x = \frac{m ^{2} + 5 m - 5 - m ^{4} + 10 m ^{3} - 5 m ^{2} + 6 m - 11}{2 ( m - 1 )}; m \neq = 1

グラフ

人気の例

0 = - 16 t^{2} + 900

4 s^{2} - 100 = 0

8 x^{2} + 12 x = - 1

- 4.9 t^{2} + 28 t = 0

18x^2-792x+6534=0

18 x^{2} - 792 x + 6534 = 0