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受欢迎的代数 >

(x^2-2x)^2=x^2

解答

(x^{2} - 2 x)^{2} = x^{2}

解答

x = 0, x = 1, x = 3

求解步骤

(x^{2} - 2 x)^{2} = x^{2}

展开

(x^{2} - 2 x)^{2} : x^{4} - 4 x^{3} + 4 x^{2}

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

将

x^{2}

para o lado esquerdo

x^{4} - 4 x^{3} + 3 x^{2} = 0

因式分解

x^{4} - 4 x^{3} + 3 x^{2} : x^{2} (x - 1) (x - 3)

x^{2} (x - 1) (x - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x - 1 = 0 or x - 3 = 0

解

x - 1 = 0 : x = 1

解

x - 3 = 0 : x = 3

解为

x = 0, x = 1, x = 3

作图

流行的例子

20 x^{3} - 24 x^{2} = 0

4 (x - 1)^{3} = 0

(x^3+1)^3-16x+8=0

(x^{3} + 1)^{3} - 16 x + 8 = 0

z^4=-2+2sqrt(3)i

z^{4} = - 2 + 23 i

x(x+7)(x^2+49)=0

x (x + 7) (x^{2} + 49) = 0