3 mũ x+4 mũ x=5 mũ x

Answer

`3^x + 4^x = 5^x`

`=> (3/5)^x + (4/5)^x = 1` `(1)`

Thay `x = 0` vào `(1)` ta có:

`(3/5)^0 + (4/5)^0 = 1`

`=> 1 + 1 = 1`

`=> 2 = 1` (Vô lý)

Thay `x = 1` vào `(1)` ta có:

`(3/5)^1 + (4/5)^1 = 1`

`=> 3/5 + 4/5 = 1`

`=> 7/5 = 1` (Vô lý)

Thay `x = 2` vào `(1)` ta có:

`(3/5)^2 + (4/5)^2 = 1`

`=> 9/25 + 16/25 = 1`

`=> 1 = 1` (Đúng)

Với `x > 2`

`=>` `(3/5)^x < (3/5)^2`

`=>` `(4/5)^x < (4/5)^2`

`=> (3/5)^x + (4/5)^x < (3/5)^2 + (4/5)^2`

`=> (3/5)^x + (4/5)^x < 9/25 + 16/25`

`=> (3/5)^x + (4/5)^x < 1` (Vô lý)

Với `x < 2`

`=>` `(3/5)^x > (3/5)^2`

`=>` `(4/5)^x > (4/5)^2`

`=> (3/5)^x + (4/5)^x > (3/5)^2 + (4/5)^2`

`=> (3/5)^x + (4/5)^x > 9/25 + 16/25`

`=> (3/5)^x + (4/5)^x > 1` (Vô lý)

Vậy `x = 2.`