Question

cần giúp gấp bài này ạ

Answer 1

a: ƯCLN(a,b)=4

=>\(\left\{{}\begin{matrix}a=4x\\b=4y\end{matrix}\right.\left(x,y\in Z^+\right)\)

a+b=32

=>4x+4y=32

=>x+y=8

mà x,y là các số nguyên dương

nên \(\left(x,y\right)\in\left\{\left(1;7\right);\left(2;6\right);\left(3;5\right);\left(4;4\right);\left(5;3\right);\left(6;2\right);\left(7;1\right)\right\}\)

=>\(\left(a,b\right)\in\left\{\left(4;28\right);\left(8;24\right);\left(12;20\right);\left(16;16\right);\left(20;12\right);\left(24;8\right);\left(28;4\right)\right\}\)

mà ƯCLN(a,b)=4

nên \(\left(a,b\right)\in\left\{\left(4;28\right);\left(12;20\right);\left(20;12\right);\left(28;4\right)\right\}\)

b: ƯCLN(a,b)=8

=>\(\left\{{}\begin{matrix}a=8c\\b=8d\end{matrix}\right.\left(c,d\in Z^+\right)\)

a+b=40

=>8c+8d=40

=>8(c+d)=40

=>c+d=5

mà c,d là các số nguyên dương

nên \(\left(c,d\right)\in\left\{\left(1;4\right);\left(4;1\right);\left(2;3\right);\left(3;2\right)\right\}\)

=>\(\left(a,b\right)\in\left\{\left(8;32\right);\left(32;8\right);\left(16;24\right);\left(24;16\right)\right\}\)

c: ƯCLN(a,b)=2

=>\(\left\{{}\begin{matrix}a=2e\\b=2f\end{matrix}\right.\left(e,f\in Z^+\right)\)

a*b=24

=>\(2\cdot e\cdot2\cdot f=24\)

=>\(4\cdot e\cdot f=24\)

=>\(e\cdot f=6\)

mà e,f là các số nguyên dương

nên \(\left(e,f\right)\in\left\{\left(1;6\right);\left(2;3\right);\left(3;2\right);\left(6;1\right)\right\}\)

=>\(\left(a,b\right)\in\left\{\left(2;12\right);\left(4;6\right);\left(6;4\right);\left(12;2\right)\right\}\)