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受欢迎的代数 >

5/2 x+1-2 x/1-2x=1-2((3-2x))/4 x^2-1

解答

\frac{5}{2} x + 1 - 2 \frac{x}{1} - 2 x = 1 - 2 \frac{( 3 - 2 x )}{4} x^{2} - 1

解答

x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

求解步骤

\frac{5}{2} x + 1 - 2 \cdot \frac{x}{1} - 2 x = 1 - 2 \cdot \frac{( 3 - 2 x )}{4} x^{2} - 1

在两边乘以

2

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

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

展开

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

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

交换两边

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

将

2

para o lado esquerdo

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

将

3 x

para o lado esquerdo

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

改写成标准形式

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

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

因式分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 1 = 0 : x = 1

解

2 x^{2} - x + 2 = 0 : x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

解为

x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

作图

流行的例子

320 = \frac{x ^{7}}{2}

x^{3} - x - 990 = 0

(2x^2-1)(x+2)(x^2-2x)(x^3+5)=0

(2 x^{2} - 1) (x + 2) (x^{2} - 2 x) (x^{3} + 5) = 0

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

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

x^3-10x^2-784=0

x^{3} - 10 x^{2} - 784 = 0