Find the range of x^2-x+1 / x^2+x+1

Answers (1)

Solution:   Let  \ \ Rightarrow hspace1cm y=fracx^2-x+1x^2+x+1\ \ Rightarrow hspace1cmy(x^2+x+1)=x^2-x+1\ \ Rightarrow hspace1cm(y-1)x^2+(y+1)x+(y-1)=0\ \ Rightarrow hspace1cmDgeq 0Rightarrow (y+1)^2-4(y-1)(y-1)geq0\ \ Rightarrow hspace1cm-3y^2+10y-3geq0Rightarrow yin[frac13,3].

      

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