tìm số tự nhiên a, b biết ưcln(a;b) = 4 và a + b = 48
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a) goi hai so la a ; b va a >b
vi UCLN(a,b)=18=>a=18k ; b=18q (trong do UCLN (k,q)=1 va k>q)
=>a+b=162
18k+18q =162
18(k+q)=162
k+q=9
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vì ƯCLN(a,b)=6 (a<b)
a=6m
b=6n
với (m,n)=1,m\(\le\)n
a+b=6m+6n=6(m+n)=84
=>m+n=14
m=1 ,n=13,=>a=6,b=78
m=3,n=11,=>a=18,b=66
m=5,n=9,=>a=30,b=54
m=7,n=7,a=42,b=42
bài còn lại cũng tương tự
Đặt \(a=4m,b=4n,\left(m,n\right)=1\).
\(a+b=4m+4n=48\Leftrightarrow m+n=12\)
mà \(\left(m,n\right)=1\)nên ta có bảng giá trị: