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Find the minimum value of f(x)=x^2-x+1÷x^2+x+1

Find the minimum value of f(x)=x^2-x+1÷x^2+x+1

Grade:11

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
f'(x)=0 imply (2x-1)(x^2+x+1) - (2x+1)(x^2-x+1)=0
solving gives, x=1
lokesh palingi
44 Points
10 years ago
y=(x^2-x+1)/(x^2+x+1) yx^2+yx+y=x^2-x+1 (y-1)x^2+(y+1)x+y-1=0 since x belong to R Therefore, Discriminant>=0 (y+1)^2-4(y-1)(y-1)>=0 y^2+2y+1-4y^2+8y-4>=0 -3y^2+10y-3>=0 3y^2-10y+3<=0 (y-3)(3y-1)<=0 y belong to 1/3 to 3 so minimum value is 1/3

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