`d)\sqrt{4(x^2-1)}-2\sqrt{15}=0`
Đk: `x^2-1>=0`
`<=>(x-1)(x+1)>=0`
`<=>[({(x-1>=0),(x+1>=0):}),({(x-1<=0),(x+1<=0):}):}`
`<=>[({(x>=1),(x>=-1):}),({(x<=1),(x<=-1):}):}`
`<=>[(x>=1),(x<=-1):}`
Vậy `ĐK: x>=1` hoặc `x<=-1`
`\sqrt{4(x^2-1)}=2\sqrt{15}`
`<=>2\sqrt{x^2-1}=2\sqrt{15}`
`<=>\sqrt{x^2-1}=\sqrt{15}`
`<=>x^2-1=15`
`<=>x^2=16`
`<=>x=+-4(tm)`
Vậy `S={+-4}`
`e)\frac{\sqrt{x}-1}{\sqrt{x}+3}=\frac{\sqrt{x}-2}{\sqrt{x}+1}(x>=0)`
`<=>(\sqrt{x}-1)(\sqrt{x}+1)=(\sqrt{x}+3)(\sqrt{x}-2)`
`<=>x-1=x+\sqrt{x}-6`
`<=>\sqrt{x}=-1+6`
`<=>\sqrt{x}=5`
`<=>x=25(tm)`
Vậy `S={25}`
`f)\sqrt{x^2-25}-\sqrt{x-5}=0(x>=5)`
`<=>\sqrt{(x-5)(x+5)}-\sqrt{x-5}=0`
`<=>\sqrt{x-5}(\sqrt{x+5}-1)=0`
`<=>[(\sqrt{x-5}=0),(\sqrt{x+5}=1):}`
`<=>[(x-5=0),(x+5=1):}`
`<=>[(x=5(tm)),(x=-4(ktm)):}`
Vậy `S={5}`
