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受欢迎的代数 >

8n^3-4n^2=18n-9

解答

8 n^{3} - 4 n^{2} = 18 n - 9

解答

n = \frac{1}{2}, n = - \frac{3}{2}, n = \frac{3}{2}

+1

十进制

n = 0.5, n = - 1.5, n = 1.5

求解步骤

8 n^{3} - 4 n^{2} = 18 n - 9

将

9

para o lado esquerdo

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

将

18 n

para o lado esquerdo

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

改写成标准形式

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

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

因式分解

8 n^{3} - 4 n^{2} - 18 n + 9 : (2 n - 1) (2 n + 3) (2 n - 3)

(2 n - 1) (2 n + 3) (2 n - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

2 n - 1 = 0 or 2 n + 3 = 0 or 2 n - 3 = 0

解

2 n - 1 = 0 : n = \frac{1}{2}

解

2 n + 3 = 0 : n = - \frac{3}{2}

解

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

解为

n = \frac{1}{2}, n = - \frac{3}{2}, n = \frac{3}{2}

作图

流行的例子

x^{3} - 8 x - 3 = 0

15.625 = s^{3}

x^4-5x^2+2x+11=0

x^{4} - 5 x^{2} + 2 x + 11 = 0

(x - 1)^{3} - 54 = 0

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