Question

[mechua]

tìm a,b thuộcn biết:

ý a(a+b=128 và ƯCLN(a,b)=16)

ý b(a . b=216 và ƯCLN (a,b)=6)

ý c(a . b=2700 và BCNN (a,b)=900)

Answer 1

[Nguyễn Thanh Hằng]

a/ \(ƯCLN\left(a,b\right)=16\) \(\Leftrightarrow\left\{{}\begin{matrix}a=16.a_1\\b=16.b_1\end{matrix}\right.\) \(\left(a_1;b_1\right)=1\) (1)

Thay \(\left(1\right)\) vào \(a+b=128\)

\(\Leftrightarrow a+b=16.a_1+16.b_1=128\)

\(\Leftrightarrow16\left(a_1+b_1\right)=128\)

\(\Leftrightarrow a_1+b_1=8\)

Mà \(\left(a_1;b_1\right)=1\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a_1=1\\b_1=7\end{matrix}\right.\\\left\{{}\begin{matrix}a_1=3\\b_1=5\end{matrix}\right.\\\left\{{}\begin{matrix}a_1=7\\b_1=1\end{matrix}\right.\\\left\{{}\begin{matrix}a_1=5\\b_1=3\end{matrix}\right.\end{matrix}\right.\)

Mà \(\left\{{}\begin{matrix}a=16.a_1\\b=16.b_1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a=16\\b=112\end{matrix}\right.\\\left\{{}\begin{matrix}a=48\\b=80\end{matrix}\right.\\\left\{{}\begin{matrix}a=112\\b=16\end{matrix}\right.\\\left\{{}\begin{matrix}a=80\\b=48\end{matrix}\right.\end{matrix}\right.\)

Vậy ..

Answer 2

[Dương Công Khoa]

cho mình hỏi a,b là số chung à