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人気のある代数 >

(m^2-1)x^2+9=2(3m+1)x

解

(m^{2} - 1) x^{2} + 9 = 2 (3 m + 1) x

解

x = \frac{2 + 6 m + 24 m + 40}{2 ( m ^{2} - 1 )}, x = \frac{2 + 6 m - 24 m + 40}{2 ( m ^{2} - 1 )}; m \neq = 1, m \neq = - 1

解答ステップ

(m^{2} - 1) x^{2} + 9 = 2 (3 m + 1) x

拡張

2 (3 m + 1) x : 6 m x + 2 x

(m^{2} - 1) x^{2} + 9 = 6 m x + 2 x

2 x

を左側に移動します

(m^{2} - 1) x^{2} + 9 - 2 x = 6 m x

6 m x

を左側に移動します

(m^{2} - 1) x^{2} + 9 - 2 x - 6 m x = 0

標準的な形式で書く

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

(m^{2} - 1) x^{2} - (2 + 6 m) x + 9 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 2 - 6 m ) \pm ( - 2 - 6 m ) ^{2} - 4 ( m ^{2} - 1 ) \cdot 9}{2 ( m ^{2} - 1 )}

簡素化

(- 2 - 6 m)^{2} - 4 (m^{2} - 1) \cdot 9 : 24 m + 40

x_{1, 2} = \frac{- ( - 2 - 6 m ) \pm 24 m + 40}{2 ( m ^{2} - 1 )}; m \neq = 1, m \neq = - 1

解を分離する

x_{1} = \frac{- ( - 2 - 6 m ) + 24 m + 40}{2 ( m ^{2} - 1 )}, x_{2} = \frac{- ( - 2 - 6 m ) - 24 m + 40}{2 ( m ^{2} - 1 )}

x = \frac{- ( - 2 - 6 m ) + 24 m + 40}{2 ( m ^{2} - 1 )} : \frac{2 + 6 m + 24 m + 40}{2 ( m ^{2} - 1 )}

x = \frac{- ( - 2 - 6 m ) - 24 m + 40}{2 ( m ^{2} - 1 )} : \frac{2 + 6 m - 24 m + 40}{2 ( m ^{2} - 1 )}

二次equationの解:

x = \frac{2 + 6 m + 24 m + 40}{2 ( m ^{2} - 1 )}, x = \frac{2 + 6 m - 24 m + 40}{2 ( m ^{2} - 1 )}; m \neq = 1, m \neq = - 1

グラフ

人気の例

solvefor x,(x/2)^2+y^2=r^2

so l v e f or x, (\frac{x}{2})^{2} + y^{2} = r^{2}

x^{2} + 10 x + 9 = - 7

m^{2} + 27 = - 12 m

solvefor x,2x^2+4xy+2y^2-5x+4y+7=0

so l v e f or x, 2 x^{2} + 4 x y + 2 y^{2} - 5 x + 4 y + 7 = 0

16 y^{2} - 361 = 0