`8,`
`A=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}`
`A^2=4+\sqrt{10+2\sqrt{5}}+4-\sqrt{10+2\sqrt{5}}+2\sqrt{(4-\sqrt{10+2\sqrt{5}})(4+\sqrt{10+2\sqrt{5}})`
`A^2=8+2\sqrt{16-(10+2\sqrt{5})}`
`A^2=8+2\sqrt{6-2\sqrt{5}}`
`A^2=8+2\sqrt{(\sqrt{5}-1)^2}`
`A^2=8+2(\sqrt{5}-1)`
`A^2=8+2\sqrt{5}-2`
`A^2=6+2\sqrt{5}`
`A^2=(\sqrt{5}+1)^2`
`-> A=\sqrt{5}+1`
`9,`
`a) 5\sqrt{2}-\sqrt{15}+5\sqrt{3}-\sqrt{10}`
`=(5\sqrt{2}-\sqrt{10})+(5\sqrt{3}-\sqrt{15})`
`=\sqrt{10}(\sqrt{5}-1)+\sqrt{15}(\sqrt{5}-1)`
`=(\sqrt{5}-1)(\sqrt{10}+\sqrt{15})`
`b) xy-y\sqrt{x}+\sqrt{x}-1` (`x;y>=0`)
`=\sqrt{x}y(\sqrt{x}-1)+(\sqrt{x}-1)`
`=(\sqrt{x}-1)(y\sqrt{x}+1)`
`c) \sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}` (`x;y>=0`)
`=(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y)+\sqrt{xy}(\sqrt{x}-\sqrt{y})`
`=(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y+\sqrt{xy})`
`=(\sqrt{x}-\sqrt{y})(x+2\sqrt{xy}+y)`
`=(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})^2`
`d) \sqrt{x^2-y^2}-x+y` (`|x|>=|y|`)
`=\sqrt{(x-y)(x+y)}-(x-y)`
`=\sqrt{x-y}(\sqrt{x+y}-\sqrt{x-y})`
`10,`
`a) \sqrt{x^2-2x+1}-2=0`
`<=> \sqrt{(x-1)^2}=2`
`<=> |x-1|=2`
`<=> [(x-1=2),(x-1=-2):}`
`<=> [(x=3),(x=-1):}`
Vậy `S={3;-1}`
`b) (2+\sqrt{x})(1+\sqrt{x})=x+5` ĐK:`x>=0`
`<=> 2+2\sqrt{x}+\sqrt{x}+x=x+5`
`<=> x+3\sqrt{x}-x=5-2`
`<=> 3\sqrt{x}=3`
`<=> \sqrt{x}=1`
`<=> x=1 (\text{tm})`
Vậy `S={1}`
