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受欢迎的代数 >

ax^2-x-a^2x+a=0

解答

a x^{2} - x - a^{2} x + a = 0

解答

x = a, x = \frac{1}{a}; a \neq = 0

求解步骤

a x^{2} - x - a^{2} x + a = 0

改写成标准形式

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

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

使用求根公式求解

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

化简

(- 1 - a^{2})^{2} - 4 aa : (a + 1) (a - 1)

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

将解分隔开

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

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

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

二次方程组的解是:

x = a, x = \frac{1}{a}; a \neq = 0

作图

流行的例子

x^{2} - 5 x - 1 = - 1

M=(x+1)^2+(x-1)^2-2

M = (x + 1)^{2} + (x - 1)^{2} - 2

solvefor x,y=4-((x-2)^2)/4

so l v e f or x, y = 4 - \frac{( x - 2 ) ^{2}}{4}

solvefor x,4x^2+36y^2+9z^2-1=0

so l v e f or x, 4 x^{2} + 36 y^{2} + 9 z^{2} - 1 = 0

8 x^{2} + 3 x = 4 x^{2} - x