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受欢迎的 Geometry >

solvefor x,x+1=u(x)^2

解答

求解

x, x + 1 = u (x)^{2}

解答

x = \frac{1 + 1 + 4 u}{2 u}, x = \frac{1 - 1 + 4 u}{2 u}; u \neq = 0

求解步骤

x + 1 = u x^{2}

交换两边

u x^{2} = x + 1

将

1

para o lado esquerdo

u x^{2} - 1 = x

将

x

para o lado esquerdo

u x^{2} - 1 - x = 0

改写成标准形式

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

u x^{2} - x - 1 = 0

使用求根公式求解

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

化简

(- 1)^{2} - 4 u (- 1) : 1 + 4 u

x_{1, 2} = \frac{- ( - 1 ) \pm 1 + 4 u}{2 u}; u \neq = 0

将解分隔开

x_{1} = \frac{- ( - 1 ) + 1 + 4 u}{2 u}, x_{2} = \frac{- ( - 1 ) - 1 + 4 u}{2 u}

x = \frac{- ( - 1 ) + 1 + 4 u}{2 u} : \frac{1 + 1 + 4 u}{2 u}

x = \frac{- ( - 1 ) - 1 + 4 u}{2 u} : \frac{1 - 1 + 4 u}{2 u}

二次方程组的解是:

x = \frac{1 + 1 + 4 u}{2 u}, x = \frac{1 - 1 + 4 u}{2 u}; u \neq = 0

作图

流行的例子

4x^2+12x+48y-159=0

4 x^{2} + 12 x + 48 y - 159 = 0

x^{2} - 2 x + 6 y + 13 = 0

y^{2} = - 40 x

y > - x^{2} - 4 x - 7

(y+3)^2=12(x+1)

(y + 3)^{2} = 12 (x + 1)