(3x^2-2x)^2-6(3x^2-2x)+5=0解方程

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(3x^2-2x)^2-6(3x^2-2x)+5=0解方程
(3x^2-2x)^2-6(3x^2-2x)+5=0解方程

(3x^2-2x)^2-6(3x^2-2x)+5=0解方程
(3x^2-2x)^2-6(3x^2-2x)+5=0
(3x^2-2x-5)(3x^2-2x-1)=0
(3x-5)(x+1)(3x+1)(x-1)=0
x1=5/3 x2=-1 x3=-1/3 x4=1
如果本题有什么不明白可以追问,

(3x^2-2x)^2-6(3x^2-2x)+5=0
(3x^2-2x-1)(3x^2-2x-5)=0
(3x+1)(x-1)(x+1)(3x-5)=0
所以
x=-1/3或x=1或x=-1或x=5/3


令t=3x^2-2x
所以t^2-6t+5=0
t1=1,t2=5
3x^2-2x-1=0或3x^2-2x-5=0
x1=1,x2=-1/3,x3=-1,x4=5/3

(3x^2-2x)^2-6(3x^2-2x)+5=0
[(3x^2-2x)-1][(3x^2-2x)-5]=0
(3x^2-2x-1)(3x^2-2x-5)=0
3x^2-2x-1=0或3x^2-2x-5=0
(3x+1)(x-1)=0或 (3x-5)(x+1)=0
x=-1/3或 x=1或, x=5/3 或x=-1

令3x^2-2x=n 原式可化为
n^2-6n+5=0
解得n=5或n=1
(1)当n=5时,有3x^2-2x=5,解得x=5/3或x=-1
(2)当n=1时,有3x^2-2x=1,解得x=1或x=-1/3
综上方程有四个解,分别是x=-1,x=-1/3,x=1,x=5/3

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