`#tnvt`
`2x-x^2+y-y^2-5`
`=-x^2+2x-1-y^2+y-1/4-15/4`
`=-(x^2-2x+1)-(y^2-y+1/4)-15/4`
`=-(x-1)^2-(y-1/2)^2-15/4`
`=-[(x-1)^2+(y-1/2)^2]-15/4`
`∀x,y\inRR,` ta có: `{((x-1)^2>=0),((y-1/2)^2>=0):}`
`<=>(x-1)^2+(y-1/2)^2>=0`
`<=>-[((x-1)^2+(y-1/2)^2]<=0`
`<=>-[(x-1)^2+(y-1/2)^2]-15/4<=-15/4<0`
`=>2x-x^2+y-y^2-5<0∀x,y`
`->đpcm`