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受欢迎的代数 >

4x^2-9=(2x^3)(2x-3)

解答

4 x^{2} - 9 = (2 x^{3}) (2 x - 3)

解答

x = \frac{3}{2}, x \approx 1.43112 \dots

+1

十进制

x = 1.5, x = 1.43112 \dots

求解步骤

4 x^{2} - 9 = (2 x^{3}) (2 x - 3)

展开

(2 x^{3}) (2 x - 3) : 4 x^{4} - 6 x^{3}

4 x^{2} - 9 = 4 x^{4} - 6 x^{3}

交换两边

4 x^{4} - 6 x^{3} = 4 x^{2} - 9

将

9

para o lado esquerdo

4 x^{4} - 6 x^{3} + 9 = 4 x^{2}

将

4 x^{2}

para o lado esquerdo

4 x^{4} - 6 x^{3} + 9 - 4 x^{2} = 0

改写成标准形式

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

4 x^{4} - 6 x^{3} - 4 x^{2} + 9 = 0

因式分解

4 x^{4} - 6 x^{3} - 4 x^{2} + 9 : (2 x - 3) (2 x^{3} - 2 x - 3)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

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

解

2 x^{3} - 2 x - 3 = 0 : x \approx 1.43112 \dots

解为

x = \frac{3}{2}, x \approx 1.43112 \dots

作图

流行的例子

8 x^{3} = (- 2 x) (A)

9x^3-18x^2-4x+8=0

9 x^{3} - 18 x^{2} - 4 x + 8 = 0

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

-x^3+2x^2+4x-8=0

- x^{3} + 2 x^{2} + 4 x - 8 = 0

9 = x^{3} + x