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受欢迎的代数 >

x^3+x^2=49x+49

解答

x^{3} + x^{2} = 49 x + 49

解答

x = - 1, x = - 7, x = 7

求解步骤

x^{3} + x^{2} = 49 x + 49

将

49

para o lado esquerdo

x^{3} + x^{2} - 49 = 49 x

将

49 x

para o lado esquerdo

x^{3} + x^{2} - 49 - 49 x = 0

改写成标准形式

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

x^{3} + x^{2} - 49 x - 49 = 0

因式分解

x^{3} + x^{2} - 49 x - 49 : (x + 1) (x + 7) (x - 7)

(x + 1) (x + 7) (x - 7) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 1 = 0 or x + 7 = 0 or x - 7 = 0

解

x + 1 = 0 : x = - 1

解

x + 7 = 0 : x = - 7

解

x - 7 = 0 : x = 7

解为

x = - 1, x = - 7, x = 7

作图

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