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受欢迎的代数 >

2x^3-4x^2+3x=1

解答

2 x^{3} - 4 x^{2} + 3 x = 1

解答

x = 1, x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

求解步骤

2 x^{3} - 4 x^{2} + 3 x = 1

将

1

para o lado esquerdo

2 x^{3} - 4 x^{2} + 3 x - 1 = 0

因式分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 1 = 0 : x = 1

解

2 x^{2} - 2 x + 1 = 0 : x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

解为

x = 1, x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

作图

流行的例子

-2x(5x-8)(49x^2-9)=0

- 2 x (5 x - 8) (49 x^{2} - 9) = 0

i x^{6} - 1 = 0

w^{3} - 2 w^{2} + w = 2

x^{6} + 7 2^{3} + 512 = 0

k^{3} = 8