x,के सभी वास्तविक मानों के लिए `(1-x+x^2)/(1+x+x^2)` का न्यूनतम मान है :

Options

A. `0`
B. `1//3`
C. `1`
D. `3`

Answer

B

Explanation

Let `y=(1-x+x^(2))/(1+x+x^(2))=1-(2x)/(1+x+x^(2))=1-2/(1//x+1+x)`
`implies y=-1-2/t`, where `t=1/x+1+x`
Now `y` is minimum when `2/t` is maximum `impliest` is minimum
`:.(dt)/(dx)=-1/(x^(2))+1`
Put `(dt)/(dx)=0implies(-1)/(x^(2))+1=0impliesx=1`
`implies(d^(2)t)/(dx^(2))=2/(x^(3))`
For `x=1,(d^(2)t)/(dx^(2))gt0`
`:.` Minimum value of `y` is
`1-2/(1+1+1)=1-2/3=1/3`