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受欢迎的代数 >

solvefor x,x^3+2x^2=9x+18

解答

求解

x, x^{3} + 2 x^{2} = 9 x + 18

解答

x = - 2, x = - 3, x = 3

求解步骤

x^{3} + 2 x^{2} = 9 x + 18

将

18

para o lado esquerdo

x^{3} + 2 x^{2} - 18 = 9 x

将

9 x

para o lado esquerdo

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

改写成标准形式

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

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

因式分解

x^{3} + 2 x^{2} - 9 x - 18 : (x + 2) (x + 3) (x - 3)

(x + 2) (x + 3) (x - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 2 = 0 or x + 3 = 0 or x - 3 = 0

解

x + 2 = 0 : x = - 2

解

x + 3 = 0 : x = - 3

解

x - 3 = 0 : x = 3

解为

x = - 2, x = - 3, x = 3

作图

流行的例子

x^3+7x^2+16x+12=0

x^{3} + 7 x^{2} + 16 x + 12 = 0

c^{3} = 2

x - 3 x^{5} - \frac{1}{4} = 0

y^{14}+12y=-16+9y

y^{14} + 12 y = - 16 + 9 y

171887=9477592-30x-4536x^4

171887 = 9477592 - 30 x - 4536 x^{4}