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受欢迎的代数 >

((x+1)(2x+3)(x+2))/6 =((x+1)^2(2x+2))/6

解答

\frac{( x + 1 ) ( 2 x + 3 ) ( x + 2 )}{6} = \frac{( x + 1 ) ^{2} ( 2 x + 2 )}{6}

解答

x = - 1, x = - \frac{4}{3}

+1

十进制

x = - 1, x = - 1.33333 \dots

求解步骤

\frac{( x + 1 ) ( 2 x + 3 ) ( x + 2 )}{6} = \frac{( x + 1 ) ^{2} ( 2 x + 2 )}{6}

在两边乘以

6

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

展开

(x + 1) (2 x + 3) (x + 2) : 2 x^{3} + 9 x^{2} + 13 x + 6

展开

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

2 x^{3} + 9 x^{2} + 13 x + 6 = 2 x^{3} + 6 x^{2} + 6 x + 2

两边减去

2 x^{3} + 6 x^{2} + 6 x + 2

2 x^{3} + 9 x^{2} + 13 x + 6 - (2 x^{3} + 6 x^{2} + 6 x + 2) = 2 x^{3} + 6 x^{2} + 6 x + 2 - (2 x^{3} + 6 x^{2} + 6 x + 2)

化简

3 x^{2} + 7 x + 4 = 0

使用求根公式求解

x_{1, 2} = \frac{- 7 \pm 7 ^{2} - 4 \cdot 3 \cdot 4}{2 \cdot 3}

7^{2} - 4 \cdot 3 \cdot 4 = 1

x_{1, 2} = \frac{- 7 \pm 1}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- 7 + 1}{2 \cdot 3}, x_{2} = \frac{- 7 - 1}{2 \cdot 3}

x = \frac{- 7 + 1}{2 \cdot 3} : - 1

x = \frac{- 7 - 1}{2 \cdot 3} : - \frac{4}{3}

二次方程组的解是:

x = - 1, x = - \frac{4}{3}

作图

流行的例子

化简 (28)/(-4)

s im pl i f y \frac{28}{- 4}

s im pl i f y - \frac{5}{2} + 2

3 x + 1 \geq 5

x = 2^{- 3}

- 22 = y - 19