zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

(3x-1)^2=(3x-1)^3

解答

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

解答

x = \frac{1}{3}, x = \frac{2}{3}

+1

十进制

x = 0.33333 \dots, x = 0.66666 \dots

求解步骤

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

展开

(3 x - 1)^{2} : 9 x^{2} - 6 x + 1

展开

(3 x - 1)^{3} : 27 x^{3} - 27 x^{2} + 9 x - 1

9 x^{2} - 6 x + 1 = 27 x^{3} - 27 x^{2} + 9 x - 1

交换两边

27 x^{3} - 27 x^{2} + 9 x - 1 = 9 x^{2} - 6 x + 1

将

1

para o lado esquerdo

27 x^{3} - 27 x^{2} + 9 x - 2 = 9 x^{2} - 6 x

将

6 x

para o lado esquerdo

27 x^{3} - 27 x^{2} + 15 x - 2 = 9 x^{2}

将

9 x^{2}

para o lado esquerdo

27 x^{3} - 36 x^{2} + 15 x - 2 = 0

因式分解

27 x^{3} - 36 x^{2} + 15 x - 2 : (3 x - 1)^{2} (3 x - 2)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

3 x - 1 = 0 or 3 x - 2 = 0

解

3 x - 1 = 0 : x = \frac{1}{3}

解

3 x - 2 = 0 : x = \frac{2}{3}

解为

x = \frac{1}{3}, x = \frac{2}{3}

作图

流行的例子

12 x^{3} - 9 x + 2 = 0

3x^3+x^2-20x+12=0

3 x^{3} + x^{2} - 20 x + 12 = 0

4 (x^{6} + 5) = 2 x + 10

solvefor y,u=y^3

so l v e f or y, u = y^{3}

(1 + x)^{5} = 4