Question

tìm MIN

A=(x^2 -x +1)/(x+1)^2

nhanh lên nha

mk cần gấp

Answer 1

Sửađề: \(A=\dfrac{x^2+x+1}{\left(x+1\right)^2}\)

\(A=\dfrac{x^2+2x+1-x}{\left(x+1\right)^2}=1-\dfrac{x}{\left(x+1\right)^2}\)

\(=1-\dfrac{x+1-1}{\left(x+1\right)^2}\)

\(=1-\dfrac{1}{x+1}+\dfrac{1}{\left(x+1\right)^2}\)

Đặt 1/x+1=a

=>A=a^2-a+1=(a-1/2)^2+3/4>=3/4

Dấu = xảy ra khi a=1/2

=>x+1=2

=>x=1