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受欢迎的代数 >

2x^3+16=x^2+32x

解答

2 x^{3} + 16 = x^{2} + 32 x

解答

x = \frac{1}{2}, x = - 4, x = 4

+1

十进制

x = 0.5, x = - 4, x = 4

求解步骤

2 x^{3} + 16 = x^{2} + 32 x

将

32 x

para o lado esquerdo

2 x^{3} + 16 - 32 x = x^{2}

将

x^{2}

para o lado esquerdo

2 x^{3} + 16 - 32 x - x^{2} = 0

改写成标准形式

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

2 x^{3} - x^{2} - 32 x + 16 = 0

因式分解

2 x^{3} - x^{2} - 32 x + 16 : (2 x - 1) (x + 4) (x - 4)

(2 x - 1) (x + 4) (x - 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

2 x - 1 = 0 or x + 4 = 0 or x - 4 = 0

解

2 x - 1 = 0 : x = \frac{1}{2}

解

x + 4 = 0 : x = - 4

解

x - 4 = 0 : x = 4

解为

x = \frac{1}{2}, x = - 4, x = 4

作图

流行的例子

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2 b^{3} + 5 = 2 (3)^{3} + 5

2 - y^{2} = y^{4}

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30 x + 27 x^{2} - 3 x^{3} = 0

x(x^2-49)(x^2+81)=0

x (x^{2} - 49) (x^{2} + 81) = 0