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受欢迎的代数 >

-12x^2(x^3+2)=0

解答

- 12 x^{2} (x^{3} + 2) = 0

解答

x = 0, x = - 32, x = \frac{3 2}{2} + i \frac{3 2 ^{\frac{2}{3}}}{2}, x = \frac{3 2}{2} - i \frac{3 2 ^{\frac{2}{3}}}{2}

求解步骤

- 12 x^{2} (x^{3} + 2) = 0

因式分解

- 12 x^{2} (x^{3} + 2) : - 12 x^{2} (x + 32) (x^{2} - 32 x + 2^{\frac{2}{3}})

- 12 x^{2} (x + 32) (x^{2} - 32 x + 2^{\frac{2}{3}}) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x + 32 = 0 or x^{2} - 32 x + 2^{\frac{2}{3}} = 0

解

x + 32 = 0 : x = - 32

解

x^{2} - 32 x + 2^{\frac{2}{3}} = 0 : x = \frac{3 2}{2} + i \frac{3 2 ^{\frac{2}{3}}}{2}, x = \frac{3 2}{2} - i \frac{3 2 ^{\frac{2}{3}}}{2}

解为

x = 0, x = - 32, x = \frac{3 2}{2} + i \frac{3 2 ^{\frac{2}{3}}}{2}, x = \frac{3 2}{2} - i \frac{3 2 ^{\frac{2}{3}}}{2}

作图

流行的例子

x^{3} + 2 x - 42 = 0

50(1+r)^{12}=10

50 (1 + r)^{12} = 10

solvefor x,x^3-x^2-10x-8=0

so l v e f or x, x^{3} - x^{2} - 10 x - 8 = 0

p^{3} - 3 p - 88 = 0

solvefor x,x^{20}+y^5=3000

so l v e f or x, x^{20} + y^{5} = 3000