Question

1.gia tri nho nhat cua x^2-x+1

2. gia tri nho nhat cua x^2+10x+2041

 

Answer 1

Bài 1:

\(x^2-x+1=x^2-x+\frac{1}{4}+\frac{3}{4}\)

\(=\left(x^2-x+\frac{1}{4}\right)+\frac{3}{4}\)

\(=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)

Dấu "=" khi \(x=\frac{1}{2}\)

Vậy \(Min=\frac{3}{4}\) khi \(x=\frac{1}{2}\)

Bài 2:

\(x^2+10x+2041=x^2+10x+25+2016\)

\(=\left(x^2+10x+25\right)+2016\)

\(=\left(x+5\right)^2+2016\ge2016\)

Dấu "=" khi \(x=-5\)

Vậy \(Min=2016\) khi \(x=-5\)