求值域y=3x²-3x+2/x²-x+1

求值域y=3x²-3x+2/x²-x+1
求值域y=3x²-3x+2/x²-x+1

求值域y=3x²-3x+2/x²-x+1
分类常数
y=3x²-3x+2/x²-x+1
=[(3x²-3x+3)-1]/(x²-x+1)
=3-1/(x²-x+1)
∵ x²-x+1=(x-1/2)²+3/4≥3/4
∴ 1/(x²-x+1)∈(0.4/3]
∴ -1/(x²-x+1)∈[-4/3,0)
∴ 3-1/(x²-x+1)∈[5/3,3)
即y=3x²-3x+2/x²-x+1的值域[5/3,3)

y=3x²-3x+2/x²-x+1
3x²-3x+2=yx²-yx+y
(3-y)x²+(y-3)x+2-y=0
判别式
△=(y-3)²-4(3-y)(2-y)
=(y-3)[y-3+4(2-y)]
=(y-3)(5-3y)≥0
(y-3)(3y-5)≤0
得 5/3≤y≤3
所以
值域为 [5/3,3]