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受欢迎的代数 >

solvefor x,x^2+mx+1=mx^2+2x

解答

x, x^{2} + m x + 1 = m x^{2} + 2 x

解答

x = \frac{1}{1 - m}, x = 1; m \neq = 1

求解步骤

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

将

2 x

para o lado esquerdo

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

将

m x^{2}

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

x = \frac{1}{1 - m}, x = 1; m \neq = 1

作图

流行的例子

w^{2} + w - 20 = 0

s^{2} + s - 4 = 0

solvefor x,4x^2-1=0

so l v e f or x, 4 x^{2} - 1 = 0

19x^2-119x+60=0

19 x^{2} - 119 x + 60 = 0

x^{2} + 1 x - 42 = 0