1/ `|x-5|=|-7|`
`=>` `|x-5|=7`
`=>` `x-5=7` `or` `x-5=-7`
`=>` `x=7+5` `or` `x=-7+5`
`=>` `x=12` `or` `x=-2`
Vậy `x=12` hoặc `x=-2`
2/
Gọi `UC(2n-1;3n+1)=d` `(d≠0)`
Vì `2n-1` ⋮ `d`
`=>` `3(2n-1)` ⋮ `d`
`=>` `6n-3` ⋮ d (*)
Vì `3n+1` ⋮ `d`
`=>` `2(3n+1)` ⋮ `d`
`=>` `6n+2` ⋮ `d` (**)
Từ (*)(**) `=>` `(6n+2-6n+3)` ⋮ d
Hay `5` ⋮ `d`
`=>` `d` ∈ `U(5)`
`=>` `d` ∈ `{-5;-1;1;5}`
`=>` `UC(2n-1;3n+1)` ∈ `{-5;-1;1;5}`
3/ `3^{2x}+3^x+3=759`
`=>` `3^x.3^x+3^x=759-3`
`=>` `3^x(3^x+1)=756`
`=>` `3^x(3^x+1)=27.28`
`=>` `3^x=27`
`=>` `3^x=3^3`
`=>` `x=3`
Vậy `x=3`
@vietkiku
