Ta có:
`10x+3sqrtx-7`
`=10x+10sqrtx-7sqrtx-7`
`=10sqrt(sqrtx+1)-7(sqrtx+1)`
`=(sqrtx+1)(10sqrtx-7)`
`xsqrtx-8`
`=sqrtx^3-8`
`=(sqrtx-2)(x+2sqrtx+4)`
`x+3sqrtx+2`
`=x+sqrtx+2sqrtx+2`
`=sqrtx(sqrtx+1)+2(sqrtx+1)`
`=(sqrtx+1)(sqrtx+2)`
`=>P=(((sqrtx-2)(x+2sqrtx+4))/((sqrtx-2)(sqrtx+2))+((10sqrtx-7)(sqrtx+1))/((sqrtx+1)(sqrtx+2))-(x-2)/(sqrtx+2)):(x+2)/(sqrtx+2)`
`P=((x+2sqrtx+4)/(sqrtx+2)+(10sqrtx-7)/(sqrtx+2)-(x-2)/(sqrtx+2))*(sqrtx+2)/(x+2)`
`P=((x+2sqrtx+4+10sqrtx-7-x+2)/(sqrtx+2))*(sqrtx+2)/(x+2)`
`P=(12sqrtx-1)/(x+2)`
`b)P+1/2`
`=(24sqrtx-2)/(2(x+2))+(x+2)/(2(x+2))`
`=(x+2+24sqrtx-2)/(2(x+2))`
`=(x+24sqrtx)/(2(x+2))>=0`
`=>P>=-1/2(1)`
Dấu "=" xảy ra khi `x=sqrtx=0<=>x=0(tmđk)`
`P-4`
`=(12sqrtx-1)/(x+2)-4`
`=(12sqrtx-1-4x-8)/(x+2)``
`=(-4x+12sqrtx-9)/(x+2)`
`=(-(4x-12sqrtx+9))/(x+2)`
`=(-(2sqrtx-3)^2)/(x+2)<=0`
`=>P<=4(2)`
Dấu "=" xảy ra khi `2sqrtx=3<=>sqrtx=3/2<=>x=9/4(tmđk)`
`(1)(2)=>-1/2<=P<=4`
