The range of x^2-x+1/x^2+x+1 , x belong to R is

Answers (1)

Solution:    

                 y=fracx^2-x+1x^2+x+1Rightarrow (y-1)x^2+(y+1)x+y-1=0

                Delta geq 0Rightarrow (y+1)^2-4(y-1)^2geq 0

                [y+1+2(y-1)][y+1-2(y-1)]geq 0

Rightarrow               (3y-1)(y-3)leq 0    ,     yin[frac13,3].

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