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受欢迎的代数 >

(m-1)*x^2-2(m-1)x+1=0

解答

(m - 1) \cdot x^{2} - 2 (m - 1) x + 1 = 0

解答

x = \frac{m - 1 + m ^{2} - 3 m + 2}{m - 1}, x = \frac{m - 1 - m ^{2} - 3 m + 2}{m - 1}; m \neq = 1

求解步骤

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

展开

(m - 1) x^{2} - 2 (m - 1) x + 1 : m x^{2} - x^{2} - 2 m x + 2 x + 1

m x^{2} - x^{2} - 2 m x + 2 x + 1 = 0

改写成标准形式

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

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

使用求根公式求解

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

化简

(- 2 m + 2)^{2} - 4 (m - 1) \cdot 1 : 2 m^{2} - 3 m + 2

x_{1, 2} = \frac{- ( - 2 m + 2 ) \pm 2 m ^{2} - 3 m + 2}{2 ( m - 1 )}; m \neq = 1

将解分隔开

x_{1} = \frac{- ( - 2 m + 2 ) + 2 m ^{2} - 3 m + 2}{2 ( m - 1 )}, x_{2} = \frac{- ( - 2 m + 2 ) - 2 m ^{2} - 3 m + 2}{2 ( m - 1 )}

x = \frac{- ( - 2 m + 2 ) + 2 m ^{2} - 3 m + 2}{2 ( m - 1 )} : \frac{m - 1 + m ^{2} - 3 m + 2}{m - 1}

x = \frac{- ( - 2 m + 2 ) - 2 m ^{2} - 3 m + 2}{2 ( m - 1 )} : \frac{m - 1 - m ^{2} - 3 m + 2}{m - 1}

二次方程组的解是:

x = \frac{m - 1 + m ^{2} - 3 m + 2}{m - 1}, x = \frac{m - 1 - m ^{2} - 3 m + 2}{m - 1}; m \neq = 1

作图

流行的例子

solvefor x,y^2=((9x^2))/(36)

so l v e f or x, y^{2} = \frac{( 9 x ^{2} )}{36}

solvefor x,w=x^2-25

so l v e f or x, w = x^{2} - 25

x (5 x - 7) = - 2

solvefor a,x=(a-b)^2

so l v e f or a, x = (a - b)^{2}

((2x+3)/4)^2= 49/25

(\frac{2 x + 3}{4})^{2} = \frac{49}{25}