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受欢迎的代数 >

-24x-24=x^3+8x^2

解答

- 24 x - 24 = x^{3} + 8 x^{2}

解答

x = - 2, x = - 3 + 3 i, x = - 3 - 3 i

求解步骤

- 24 x - 24 = x^{3} + 8 x^{2}

交换两边

x^{3} + 8 x^{2} = - 24 x - 24

将

24

para o lado esquerdo

x^{3} + 8 x^{2} + 24 = - 24 x

将

24 x

para o lado esquerdo

x^{3} + 8 x^{2} + 24 + 24 x = 0

改写成标准形式

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

x^{3} + 8 x^{2} + 24 x + 24 = 0

因式分解

x^{3} + 8 x^{2} + 24 x + 24 : (x + 2) (x^{2} + 6 x + 12)

(x + 2) (x^{2} + 6 x + 12) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 2 = 0 or x^{2} + 6 x + 12 = 0

解

x + 2 = 0 : x = - 2

解

x^{2} + 6 x + 12 = 0 : x = - 3 + 3 i, x = - 3 - 3 i

解为

x = - 2, x = - 3 + 3 i, x = - 3 - 3 i

作图

流行的例子

4 x (5 x^{2} - 3) = 0

20x=x^2(x)+36x-2x(x)(x)

20 x = x^{2} (x) + 36 x - 2 x (x) (x)

solvefor y,y^2-y^4=x

so l v e f or y, y^{2} - y^{4} = x

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

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