`abc = 1`
Ta có: `1/a + 1/b + 1/c = (abc)/a + (abc)/b + (abc)/c`
`= bc + ac + ab`
`<=> a + b + c > bc + ac + ab`
Lại có:
`(a - 1)(b - 1)(c - 1) > 0`
`<=> (ab - a - b + 1)(c - 1) > 0`
`<=> abc - ac- bc + c - ab + a + b - 1 > 0`
`<=> 1 - (ac + bc + ab) + (a + b + c) - 1 > 0`
`<=> -(ac + bc + ab) + (a + b + c) > 0`
`<=> a + b + c > ac + bc + ab`(luôn đúng)
`=> (a - 1)(b - 1)(c - 1) > 0`
`=> đpcm`
