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受欢迎的代数 >

6-3(x+1)=-4x^2(1-x)

解答

6 - 3 (x + 1) = - 4 x^{2} (1 - x)

解答

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

求解步骤

6 - 3 (x + 1) = - 4 x^{2} (1 - x)

展开

6 - 3 (x + 1) : - 3 x + 3

展开

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

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

交换两边

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

将

3

para o lado esquerdo

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

将

3 x

para o lado esquerdo

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

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

因式分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 1 = 0 : x = 1

解

4 x^{2} + 3 = 0 : x = \frac{3}{2} i, x = - \frac{3}{2} i

解为

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

作图

流行的例子

3x^4-3x^3-1x^2=0

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

z \cdot z^{3} + 15 = 16.66

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

- 3 = x^{6} - 8

x^2(x^2-4)=x^4(x^2-4)

x^{2} (x^{2} - 4) = x^{4} (x^{2} - 4)