(x^2-2)/x+2x/(x^2-2)=3怎么解

来源：百度知道编辑：UC知道时间：2024/06/02 17:05:31

设（x^2-2)/X=a
则a+2/a=3
a^2-3a+2=0
a1=2,a2=1
当a=2
（x^2-2)/X=2
x^2-2x-2=0
x1=根号3，x2=-根号3
当a=1
（x^2-2)/X=1
x^2-x-2=0
x3=2,x4=-1

(x^2-2)/x+2x/(x^2-2)=3

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

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

((x^2-2) - x)((x^2-2) - 2x) = 0

(x^2-2) - x = 0 OR (x^2-2) - 2x = 0

(x-2)(x+1) = 0 OR x-1 = +- sqrt(3)

x1 = -1

x2 = 2

x3 = 1 + sqrt(3)

x4 = 1 - sqrt(3)

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