cho Q= ( √x -2 phần x-1 trừ cho √x+2 phần x+2 √x+1)* (1-x)mũ hai phần 2 a, rút gọn Q b, tìm x để Q dương c, tìm GTNN

Đáp án:

`a)Q=((sqrtx-2)/(x-1)-(sqrtx+2)/(x+2sqrtx+1))*(1-x)^2/2`

`Q=((sqrtx-2)/((sqrtx-1)(sqrtx+1))-(sqrtx+2)/(sqrtx+1)^2)*(x-1)^2/2`

`Q=(((sqrtx-2)(sqrtx+1)-(sqrtx+2)(sqrtx-1))/((sqrtx+1)^2(sqrtx-1)))*(x-1)^2/2`

`Q=((x-sqrtx-2-x-sqrtx+2)/((sqrtx+1)^2(sqrtx-1)))*(x-1)^2/2`

`Q=(-2sqrtx)/((x-1)(sqrtx+1))*(x-1)^2/2`

`Q=-sqrtx(sqrtx-1)`

`b)Q>0`

`<=>-sqrtx(sqrtx-1)>0`

`<=>sqrtx(sqrtx-1)<0`

Vì `sqrtx>sqrtx-1`

`=>sqrtx>0,sqrtx-1<0`

`<=>0<x<1`

`c)Q=-sqrtx(sqrtx-1)`

`=-x+sqrtx`

`=-(x-sqrtx)`

`=-(x-sqrtx+1/4)+1/4`

`=-(sqrtx-1/2)^2+1/4<=1/4`

Dấu “=” xảy ra khi `sqrtx=1/2<=>x=1/4.`