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受欢迎的代数 >

n^3-n=6n^2-6

解答

n^{3} - n = 6 n^{2} - 6

解答

n = 6, n = - 1, n = 1

求解步骤

n^{3} - n = 6 n^{2} - 6

将

6

para o lado esquerdo

n^{3} - n + 6 = 6 n^{2}

将

6 n^{2}

para o lado esquerdo

n^{3} - n + 6 - 6 n^{2} = 0

改写成标准形式

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

n^{3} - 6 n^{2} - n + 6 = 0

因式分解

n^{3} - 6 n^{2} - n + 6 : (n - 6) (n + 1) (n - 1)

(n - 6) (n + 1) (n - 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

n - 6 = 0 or n + 1 = 0 or n - 1 = 0

解

n - 6 = 0 : n = 6

解

n + 1 = 0 : n = - 1

解

n - 1 = 0 : n = 1

解为

n = 6, n = - 1, n = 1

作图

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