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受欢迎的代数 >

x^2-6=6-x^3

解答

x^{2} - 6 = 6 - x^{3}

解答

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

求解步骤

x^{2} - 6 = 6 - x^{3}

交换两边

6 - x^{3} = x^{2} - 6

将

6

para o lado esquerdo

- x^{3} + 12 = x^{2}

将

x^{2}

para o lado esquerdo

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

改写成标准形式

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

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

因式分解

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

- (x - 2) (x^{2} + 3 x + 6) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 2 = 0 or x^{2} + 3 x + 6 = 0

解

x - 2 = 0 : x = 2

解

x^{2} + 3 x + 6 = 0 : x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

解为

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

作图

流行的例子

x^{4} - 2 x^{2} + a = 0

x^{10} = 3

(x - 1)^{3} = 17

(x - 1)^{3} = - 8

x^3+2x^2+3x+1=0

x^{3} + 2 x^{2} + 3 x + 1 = 0