Vì (a,b) = 16 => \(\hept{\begin{cases}a=16m\\b=16n\end{cases}\left(m,n\in N;\left(m,n\right)=1\right)}\)
Ta có: a+b=96
=> 16m+16n = 96
=> 16(m+n) = 96
=> m+n = 6
Vì a < b nên m < n
Mà (m,n) = 1
Ta có bảng:
| m | 1 |
| n | 5 |
| a | 16 |
| b | 80 |
Vậy a = 16, b = 80
Giai
Vi UCLN ( a,b ) = 16
=> ta dat a= 16x
b=16y
Voi x,y thuoc N va UCLN (x,y) = 1
a + b = 96
Thay a = 16x, b = 16y
=> 16x + 16y = 96
=> 16 . ( x + y ) = 96
=> x + y = 6
Ta lap bang :
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| y | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| a | 0 | 16 | 32 | 48 | 64 | 80 | 96 |
| b | 96 | 80 | 64 | 48 | 32 | 16 | 0 |
=> (a,b) = ( 0,96 ) ; ( 16, 80) ; ( 48,48 ) ; ( 64,32 ) ; ( 80, 16 ) ; ( 96,0 )
Vi a<b => (a,b) = ( 64,32 ) ; ( 80 ; 16 ) ; ( 96, 0 )
Vay .......
Chuc ban hoc tot !
vì ƯCLN(a,b)=16
=>a=16m , b=16n (ƯCLN (a,b)=1)
mà a+b=96 => 16m+16n=96
=>m+n=6
có:
m=1 , n=5 => a=16 , b=80
=>a=16 , b=80
