Question

tim gia tri nho nhat d=x^2+5y^2+2xy-2y+2005

Answer 1

d= x^2 + 5y^2 + 2xy - 2y + 2005 d= x^2 + 2xy + y^2 + 4y^2 - 2y + 1/4+ d= ( x+y)^2 + ( 2y - 1/2)^2 + 8019/4 > hoặc = 8019/4 dmin= 8019/4 khi y=1/4 ; x= -y = -1/4

Answer 2

d= x²  + 5y² + 2xy - 2y + 2005

d= x² + 2xy + y²  + 4y²  - 2y + \(\frac{1}{4}+\)

d= ( x+ y )²  + ( 2y - \(\frac{1}{2}\))²  + \(\frac{8019}{4}\)\(\ge\)\(\frac{8019}{4}\)

dmin= \(\frac{8019}{4}khi\hept{\begin{cases}y=\frac{1}{4}\\x=-y=\frac{-1}{4}\end{cases}}\)