Đáp án+Giải thích các bước giải:
`1)x-\sqrt{4x^2-4x+1}=-5`
`<=>x+5-\sqrt{(2x-1)^2}=0`
`<=>x+5=|2x-1|`
Vì `|2x-1|>=0`
`=>x+5>=0=>x>=-5`
`=>[(2x-1=x+5),(2x-1=-x-5):}`
`=>[(x=6(tm)),(3x=-4):}`
`=>[(x=6(tm)),(x=-4/3(tm)):}`
`=>S={6;-4/3}.`
`2)3\sqrt{9x-27}-5\sqrt{x-3}=2`
Điều kiện:`x-3>=0<=>x>=3`
`pt<=>3\sqrt{9(x-3)}-5\sqrt{x-3}=2`
`<=>9\sqrt{x-3}-5\sqrt{x-3}=2`
`<=>4\sqrt{x-3}=2`
`<=>\sqrt{x-3}=1/2`
`<=>x-3=1/4`
`<=>x=13/4(tm)`
`=>S={13/4}.`
`3)x-4\sqrt{x-3}=8`
`<=>x-3-4\sqrt{x-3}-5=0`
Đặt `t=\sqrt{x-3}(t>=0)`
`pt<=>t^2-4t-5=0`
`<=>(t+1)(t-5)=0`
`<=>t-5=0`
`<=>t=5(tm)`
`<=>\sqrt{x-3}=5`
`<=>x-3=25`
`<=>x=28(tm)`
`=>S={28}.`
`4)\sqrt{x+2}-\sqrt{x-3}=1`
Điều kiện:`{(x+2>=0),(x-3>=0):}`
`<=>{(x>=-2),(x>=3):}<=>x>=3`
`pt<=>sqrt{x+2}=sqrt{x-3}+1`
`<=>x+2=x-3+1+2sqrt{x-3}`
`<=>4=2sqrt{x-3}`
`<=>sqrt{x-3}=2`
`<=>x-3=4`
`<=>x=7(tm)`
`=>S={7}.`
