<s>[INST] Minimum value of given expression What is the minimum value of the $$ \frac {x^2 + x + 1 }  {x^2 - x + 1 } \ ?$$
I have solved by equating it to m and then discriminant greater than or equal to zero and got the answer, but can algebraic manipulation is possible 
 [/INST] let y=$\frac{x^2+x+1}{x^2-x+1}$
=>$x^2(y-1)-x(y+1)+(y-1)=0$
As x is real, the discriminant= $(y+1)^2-4(y-1)^2≥0$ 
=>$(y-3)(y-\frac{1}{3})≤0$
=>$\frac{1}{3}≤y≤3$
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