`3,`
`a) 2\sqrt{a^2}-5a\qquad(a<0)`
`=2|a|-5a`
`=-2a-5a`
`=-7a`
`b) \sqrt{25a^2}+3a\qquad (a>=0)`
`=\sqrt{(5a)^2}+3a`
`=|5a|+3a`
`=5a+3a`
`=8a`
`c) 5\sqrt{4a^6}-3a^3\qquad(a<0)`
`=5\sqrt{(2a^3)^2}-3a^3`
`=5|2a^3|-3a^3`
`=5.(-2a^3)-3a^3`
`=-10a^3-3a^3`
`=-13a^3`
`4,` Với `a>b>0` thì
`M=\sqrt{a^2-2ab+b^2}/\sqrt{a^2+2ab+b^2}+(2a)/(a+b)`
`M=\sqrt{(a-b)^2}/\sqrt{(a+b)^2}+(2a)/(a+b)`
`M=|a-b|/|a+b|+(2a)/(a+b)`
`M=(a-b)/(a+b)+(2a)/(a+b)`
`M=(a-b+2a)/(a+b)`
`M=(3a-b)/(a+b)`
Vậy `M=(3a-b)/(a+b)` với `a>b>0`
`5,` Với `1<=x<=2` thì
`A=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}`
`A=\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}`
`A=\sqrt{(\sqrt{x-1}+1)^2}+\sqrt{(\sqrt{x-1}-1)^2}`
`A=|\sqrt{x-1}+1|+|\sqrt{x-1}-1|`
`A=\sqrt{x-1}+1+1-\sqrt{x-1}`
`A=2`
Vậy `A=2` với `1<=x<=2`
