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受欢迎的代数 >

n^2+n^3=-180

解答

n^{2} + n^{3} = - 180

解答

n = - 6, n = \frac{5}{2} + i \frac{95}{2}, n = \frac{5}{2} - i \frac{95}{2}

求解步骤

n^{2} + n^{3} = - 180

将

180

para o lado esquerdo

n^{2} + n^{3} + 180 = 0

改写成标准形式

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

n^{3} + n^{2} + 180 = 0

因式分解

n^{3} + n^{2} + 180 : (n + 6) (n^{2} - 5 n + 30)

(n + 6) (n^{2} - 5 n + 30) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

n + 6 = 0 or n^{2} - 5 n + 30 = 0

解

n + 6 = 0 : n = - 6

解

n^{2} - 5 n + 30 = 0 : n = \frac{5}{2} + i \frac{95}{2}, n = \frac{5}{2} - i \frac{95}{2}

解为

n = - 6, n = \frac{5}{2} + i \frac{95}{2}, n = \frac{5}{2} - i \frac{95}{2}

作图

流行的例子

x^3+5x^2+6x=-30

x^{3} + 5 x^{2} + 6 x = - 30

4(x+4)^4-53(x+4)^2=-49

4 (x + 4)^{4} - 53 (x + 4)^{2} = - 49

0=x^3-2x^2-11x+12

0 = x^{3} - 2 x^{2} - 11 x + 12

a \cdot a \cdot a = 3 a

2x^3+3x^2-17x+12=0

2 x^{3} + 3 x^{2} - 17 x + 12 = 0