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受欢迎的代数 >

4x^4=864x

解答

4 x^{4} = 864 x

解答

x = 0, x = 6, x = - 3 + 33 i, x = - 3 - 33 i

求解步骤

4 x^{4} = 864 x

将

864 x

para o lado esquerdo

4 x^{4} - 864 x = 0

因式分解

4 x^{4} - 864 x : 4 x (x - 6) (x^{2} + 6 x + 36)

4 x (x - 6) (x^{2} + 6 x + 36) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x - 6 = 0 or x^{2} + 6 x + 36 = 0

解

x - 6 = 0 : x = 6

解

x^{2} + 6 x + 36 = 0 : x = - 3 + 33 i, x = - 3 - 33 i

解为

x = 0, x = 6, x = - 3 + 33 i, x = - 3 - 33 i

作图

流行的例子

x^4-3x^3-11x^2+3x+10=0

x^{4} - 3 x^{3} - 11 x^{2} + 3 x + 10 = 0

x^3-3x^2+5x-15=0

x^{3} - 3 x^{2} + 5 x - 15 = 0

x^3+5nx^2-4x-20n=0

x^{3} + 5 n x^{2} - 4 x - 20 n = 0

(x^{2} + 5)^{4} = 16

x^3-6x^2-5x+30=0

x^{3} - 6 x^{2} - 5 x + 30 = 0