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

Solution:   Let  $\\ \\ \Rightarrow \hspace{1cm} y=\frac{x^{2}-x+1}{x^{2}+x+1}\\ \\ \Rightarrow \hspace{1cm}y(x^{2}+x+1)=x^{2}-x+1\\ \\ \Rightarrow \hspace{1cm}(y-1)x^{2}+(y+1)x+(y-1)=0\\ \\ \Rightarrow \hspace{1cm}D\geq 0\Rightarrow (y+1)^{2}-4(y-1)(y-1)\geq0\\ \\ \Rightarrow \hspace{1cm}-3y^{2}+10y-3\geq0\Rightarrow y\in[\frac{1}{3},3].$

## Most Viewed Questions

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-