\(x^2-2y+2y^2-4x+7=\left(x^2-4x+4\right)+\left(2y^2-2y+\frac{1}{2}\right)+\frac{5}{2}\)
\(=\left(x-2\right)^2+2\left(y^2-y+\frac{1}{4}\right)+\frac{5}{2}\)
\(=\left(x-2\right)^2+2\left(y^2-2.\frac{1}{2}.y+\frac{1}{4}\right)+\frac{5}{2}\)
\(=\left(x-2\right)^2+2\left(y-\frac{1}{2}\right)^2+\frac{5}{2}\ge\frac{5}{2}\)
Dấu "=" xảy ra khi x=2 và y=1/2
tim gia tri nho nhat cua
\(\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)+\frac{1}{4}\left(x^{16}+y^{16}\right)-\left(1+x^2y^2\right)^2\)
tim gia tri nho nhat cua \(\frac{4x+1}{x^2+3}\)
Tim gia tri nho nhat va lon nhat cua bieu thuc sau: \(p=\frac{4x+3}{x^2+1}\)
tim gia tri nho nhat cua \(\frac{3}{2+\sqrt{-x^2+2x+7}}\)
tim gia tri nho nhat cua \(\frac{356+4x^4+16x^3+56x^2+80x}{x^2+2x+5}\)
Tim gia tri lon nhat va gia tri nho nhat cua bieu thuc sau: A=\(\frac{x+1}{x^2+x+1}\)
Tim gia tri nho nhat cua Q(x)= x(x-1)(x-2)(x-3)
\(\sqrt{-x^2+2x+4}\) tim gia tri nho nhat
tim gia tri nho nhat cua P=\(\frac{x+3\sqrt{x}+2}{x}\)
