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受欢迎的代数 >

(x^3-1)(x+2)(x^2+2x+4)=0

解答

(x^{3} - 1) (x + 2) (x^{2} + 2 x + 4) = 0

解答

x = 1, x = - 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}, x = - 1 + 3 i, x = - 1 - 3 i

求解步骤

(x^{3} - 1) (x + 2) (x^{2} + 2 x + 4) = 0

因式分解

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

(x - 1) (x + 2) (x^{2} + x + 1) (x^{2} + 2 x + 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 1 = 0 or x + 2 = 0 or x^{2} + x + 1 = 0 or x^{2} + 2 x + 4 = 0

解

x - 1 = 0 : x = 1

解

x + 2 = 0 : x = - 2

解

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

解

x^{2} + 2 x + 4 = 0 : x = - 1 + 3 i, x = - 1 - 3 i

解为

x = 1, x = - 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}, x = - 1 + 3 i, x = - 1 - 3 i

作图

流行的例子

x^{10} = - x, x

x^3+7x^2+9x-17=0

x^{3} + 7 x^{2} + 9 x - 17 = 0

solvefor x,8x^3-27y^2=0

so l v e f or x, 8 x^{3} - 27 y^{2} = 0

4x(7+3)=(4x^7)+(4x^3)

4 x (7 + 3) = (4 x^{7}) + (4 x^{3})

(16(16+1))/2 =a^3

\frac{16 ( 16 + 1 )}{2} = a^{3}