x^4+4x=0

解答

x^{4} + 4 x = 0

x = 0, x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i

求解步骤

x^{4} + 4 x = 0

因式分解

x^{4} + 4 x : x (x^{3} + 4)

x (x^{3} + 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} + 4 = 0

解

x^{3} + 4 = 0 : x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i

解为

x = 0, x = - 34, x = \frac{1}{3 2} - \frac{3}{3 2} i, x = \frac{1}{3 2} + \frac{3}{3 2} i

x^{3} - 4 x^{2} - 25 x = - 100

12755 = 12000 \cdot (1 + x)^{14}

4 x^{3} + 6 x^{2} - 8 x - 2 = 0

(2 x + 3) (4 x^{2} - 6 x + 9) = 0

4 w^{4} + 8 w^{3} - 17 w^{2} - 21 w - 18 = 0