`4x^2-5x-4sqrt[x-1]-2=0 (x>=1)`

`<=> 4x^2-4x+1-4sqrt[x-1]-x-3=0`

`<=> 4x^2-4x+1-x+1-4sqrt[x-1]-4=0`

`<=> (2x-1)^2-(x-1+4sqrt[x-1]+4)=0`

`<=> (2x-1)^2-(sqrt[x-1]+2)^2=0`

`<=> (2x-1-sqrt[x-1]-2)(2x-1+sqrt[x-1]+2)=0`

`<=> (2x-sqrt[x-1]-3)(2x+sqrt[x-1]+1)=0`

`<=> 2x-sqrt[x-1]-3=0` hoặc `2x+sqrt[x-1]+1=0`

TH1: `2x-sqrt[x-1]-3=0`

`<=> sqrt[x-1]=2x-3`

`=> (sqrt[x-1])^2=(2x-3)^2 (x>=3/2)`

`<=> x-1=4x^2-12x+9`

`<=> 4x^2-13x+10=0`

`<=> 4x^2-8x-5x+10=0`

`<=> 4x(x-2)-5(x-2)=0`

`<=> (4x-5)(x-2)=0`

`<=> x=5/4(text[l])` hoặc `x=2(text[n])`

TH2: `2x+sqrt[x-1]+1=0`

`<=> sqrt[x-1]=-1-2x`

Ta thấy

Vế trái có `x-1>=0 <=> x>=1`

Vế phải có `-1-2x>=0 <=> x<=-1/2`

`->` Mâu thuẫn

`->S={2}`