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受欢迎的代数 >

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

解答

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

解答

x = A, x = - A, x = i 4 A, x = - i 4 A

求解步骤

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

展开

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

A = x^{4}

交换两边

x^{4} = A

将

A

para o lado esquerdo

x^{4} - A = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - A = 0

解

u^{2} - A = 0 : u = A, u = - A

u = A, u = - A

代回

u = x^{2}

，求解

x

解

x^{2} = A : x = A, x = - A

解

x^{2} = - A : x = i 4 A, x = - i 4 A

解为

x = A, x = - A, x = i 4 A, x = - i 4 A

作图

流行的例子

c^{3} + 9 = 10

x^{4} + 4 x^{2} - 60 = 0

x + x^{3} = 2

solvefor x,x^3-49x=0

so l v e f or x, x^{3} - 49 x = 0

(1-x)(1-x)(-1-x)-i(-i)(-1-x)=0

(1 - x) (1 - x) (- 1 - x) - i (- i) (- 1 - x) = 0