Question

tìm gtnn \(5x^2+y^2+z^2-4x-2xy-z-1\)

Answer 1

Ta có:A =  5x² + y² + z² - 4x - 2xy - z - 1

A = (x² - 2xy + y²) + (4x² - 4x + 1) + (z² - z + 1/4) - 9/4

A = (x - y)² + (2x - 1)² + (z - 1/2)² - 9/4 \(\ge\)- 9/4 \(\forall\)x;y

Dấu "=" xảy ra <=> \(\hept{\begin{cases}x-y=0\\2x-1=0\\z-\frac{1}{2}=0\end{cases}}\) <=> \(\hept{\begin{cases}x=y\\x=\frac{1}{2}\\z=\frac{1}{2}\end{cases}}\) <=> x =  y = z = 1/2

Vậy MinA = -9/4 khi x = y = z = 1/2

Answer 2

=)) mình cũng làm ntn mà rút gọn ngu -9/4=-3/2 kq sai :v