Question

Tìm giá trị nhỏ nhất

\(C=2x^2-x+1\)

\(D=x^2+y^2+xy+x+y+100\)

Answer 1

\(C=2x^2-x+1=2\left(x^2-x.\frac{1}{2}+\frac{1}{2}\right)=2\left(x^2-2.x.\frac{1}{4}+\left(\frac{1}{4}\right)^2+\frac{7}{16}\right)=2\left(x-\frac{1}{4}\right)^2+\frac{7}{4}\)

Vì \(\left(x-\frac{1}{4}\right)\ge0\)

nên \(2\left(x-\frac{1}{4}\right)^2+\frac{7}{16}\ge\frac{7}{16}\)

Vậy \(Min_C=\frac{7}{16}\)khi \(x-\frac{1}{4}=0\Rightarrow x=\frac{1}{4}\)