Question

Tìm hai số nguyên dương a, b biết a + b = 128 và ƯCLN(a, b) = 16

Answer 1

https://olm.vn/hoi-dap/detail/57014713299.html

Answer 2

Vì ƯCLN(a,b) = 16 \(\Rightarrow\left\{{}\begin{matrix}a=16.m\\b=16.n\end{matrix}\right.\left(m,n\in N\right);\left(m,n=1\right)\)

Vì a + b = 128

\(\Rightarrow16.m+16.n=128\)

\(\Rightarrow16.\left(m+n\right)=128\)

\(\Rightarrow m+n=128:16\)

\(\Rightarrow m+n=8\)

Ta được \(\left\{{}\begin{matrix}m=5\\n=3\end{matrix}\right.\)

\(\left\{{}\begin{matrix}m=7\\n=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=16.5=80\\b=16.3=48\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=16.7=112\\b=16.1=16\end{matrix}\right.\)

Vậy \(\left\{{}\begin{matrix}a=80\\b=48\end{matrix}\right.\)

\(\left\{{}\begin{matrix}a=112\\b=16\end{matrix}\right.\)