a: ƯCLN(a,b)=45
=>\(\left\{{}\begin{matrix}a=45k\\b=45c\end{matrix}\right.\)
Ta có: a+b=270
=>45k+45c=270
=>45(k+c)=270
=>k+c=6
=>\(\left(k;c\right)\in\left\{\left(1;5\right);\left(2;4\right);\left(3;3\right);\left(4;2\right);\left(5;1\right)\right\}\)
=>\(\left(a,b\right)\in\left\{\left(45;225\right);\left(90;180\right);\left(135;135\right);\left(180;90\right);\left(225;45\right)\right\}\)
mà ƯCLN(a,b)=45
nên \(\left(a,b\right)\in\left\{\left(45;225\right);\left(225;45\right)\right\}\)
b: \(ƯCLN\left(a,b\right)=5\)
=>\(\left\{{}\begin{matrix}a=5k\\b=5c\end{matrix}\right.\)
\(5k\cdot5c=300\)
=>\(25\cdot k\cdot c=300\)
=>\(k\cdot c=\dfrac{300}{25}=12\)
=>\(\left(k;c\right)\in\left\{\left(1;12\right);\left(12;1\right);\left(2;6\right);\left(6;2\right);\left(3;4\right);\left(4;3\right)\right\}\)
=>\(\left(a,b\right)\in\left\{\left(5;60\right);\left(60;5\right);\left(10;30\right);\left(30;10\right);\left(15;20\right);\left(20;15\right)\right\}\)
mà ƯCLN(a,b)=5
nên \(\left(a,b\right)\in\left\{\left(5;60\right);\left(60;5\right);\left(15;20\right);\left(20;15\right)\right\}\)
