Question

tìm a,b e N* biết a>b , ab = 128 , BCNN ( a,b) = 64

Answer 1

\(a\cdot b=BCNN\left(a,b\right)\cdotƯCLN\left(a,b\right)\)

=>\(ƯCLN\left(a,b\right)=\dfrac{128}{64}=2\)

=>\(\left\{{}\begin{matrix}a=2k\\b=2e\end{matrix}\right.\)

a>b>0 nên 2k>2e>0

=>k>e>0

\(a\cdot b=128\)

=>\(2k\cdot2e=128\)

=>\(k\cdot e=\dfrac{128}{4}=32\)

mà k>e>0

nên \(\left(k,e\right)\in\left\{\left(32;1\right);\left(16;2\right);\left(8;4\right)\right\}\)

=>\(\left(a,b\right)\in\left\{\left(64;2\right);\left(16;8\right);\left(32;4\right)\right\}\)

mà BCNN(a,b)=64

nên a=64 và b=2