(u-1)^2 + (v+3/2)^2 + 11,75 \(\ge\)11,75
''='' <=> u = 1, v = -3/2
=> Min = 11,75 <=> u = 1, v = -3/2
Đặt \(A=u^2+v^2-2u+3v+15\)
\(=\left(u^2-2u+1\right)+\left(v^2+3v+\frac{9}{16}\right)+\frac{215}{16}\)
\(=\left(u-1\right)^2+\left(v+\frac{3}{4}\right)^2+\frac{215}{16}\ge\frac{215}{16}\)
Dấu "=" xảy ra khi u = 1, v = -3/4
Vậy Amin = 215/16 khi u = 1, v = -3/4
Sửa lại
\(=\left(u^2-2u+1\right)+\left(v^2+3v+\frac{9}{4}\right)+\frac{47}{4}=\left(u-1\right)^2+\left(v+\frac{3}{2}\right)^2+\frac{47}{4}\ge\frac{47}{4}\)
Dấu "=" xảy ra khi u=1,v=-3/2
Vậy Amin=47/4 khi u=1,v=-3/2
