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受欢迎的代数 >

x^3+3x^2=81x+243

解答

x^{3} + 3 x^{2} = 81 x + 243

解答

x = - 3, x = - 9, x = 9

求解步骤

x^{3} + 3 x^{2} = 81 x + 243

将

243

para o lado esquerdo

x^{3} + 3 x^{2} - 243 = 81 x

将

81 x

para o lado esquerdo

x^{3} + 3 x^{2} - 243 - 81 x = 0

改写成标准形式

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

x^{3} + 3 x^{2} - 81 x - 243 = 0

因式分解

x^{3} + 3 x^{2} - 81 x - 243 : (x + 3) (x + 9) (x - 9)

(x + 3) (x + 9) (x - 9) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 3 = 0 or x + 9 = 0 or x - 9 = 0

解

x + 3 = 0 : x = - 3

解

x + 9 = 0 : x = - 9

解

x - 9 = 0 : x = 9

解为

x = - 3, x = - 9, x = 9

作图

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