Đáp án:
`N_(min) = -1/2 <=> x = 9/4; y = 1/4`
Giải thích các bước giải:
`N = x - 2sqrt(xy) + 3y - 2sqrtx +1`
`N = x-2sqrtxy + y +2y - 2sqrtx +1`
`N = (x-2sqrt(xy) + y) + 2y - 2sqrtx +1`
`N = [(sqrtx + sqrty)^2 - 2(sqrtx - sqrty)+1] - 2sqrty + 2y`
`N = (sqrtx - sqrty -1)^2 + (2y - 2sqrty+1/2)-1/2`
`N = (sqrtx - sqrty - 1)^2 + 1/2(2sqrty -1)^2 -1/2 ge -1/2`
`N_(min) = -1/2 <=>`$ \left\{\begin{matrix} \sqrt{x} -\sqrt{y} -1 =0\\\\2\sqrt{y} -1=0 \end{matrix}\right.$ `<=>` $ \left\{\begin{matrix} x=\dfrac{9}{4}\\\\y = \dfrac{1}{4} \end{matrix}\right.$
Vậy `N_(min) = -1/2 <=> x = 9/4 ; y =1/4`
