`k)`
\(K=x^2+2y^2+2xy+2x+4y+2025\\ =\left(x^2+2xy+y^2\right)+\left(y^2+2y+1\right)+2x+2y+2025\\ =[\left(x+y\right)^2+2\left(x+y\right)+1]+\left(y+1\right)^2+2024\\ =\left(x+y+1\right)^2+\left(y+1\right)^2+2024\)
`AA x;y` ta có : `{:((x+y+1)^2>=0),((y+1)^2>=0):}}`
`=>(x+y+1)^2+(y+1)^2>=0`
`=>(x+y+1)^2+(y+1)^2+2024>=0+2024`
hay `K>=2024`
Dấu `"="` xảy ra khi \(\left\{{}\begin{matrix}\left(x+y+1\right)^2=0\\\left(y+1\right)^2=0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x+y+1=0\\y+1=0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x=0\\y=-1\end{matrix}\right.\)
Vậy `Mi n K =2024` khi `x=0; y=-1`
`h)`
\(H=\left(x-2\right)\left(x-3\right)\left(x-6\right)\left(x+1\right)\\ =\left(x^2-5x+6\right)\left(x^2-5x-6\right)\\ =\left(x^2-5x\right)^2-36\)
`AA x` ta có `(x^2-5x)^2>=0`
`=>(x^2-5x)^2-36>=0-36`
hay `H>=-36`
Dấu `" = "` xảy ra khi `(x^2-5x)^2=0`
`x^2-5x=0`
`x(x-5)=0`
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
Vậy `Mi n H=-36` khi `x=0` hoặc `x=-5`
