Quy đồng lên, ta có :5x+5y=xy

\(\rightarrow\) x (5-y) = -5y

\(\rightarrow\)

\(\rightarrow\)

\(\rightarrow\)

\(\rightarrow\)

x nguyên \(\rightarrow\dfrac{-25}{5-y}\) nguyên \(\rightarrow\) 5-y \(\in\) Ư(25)

Ư(25)={-25,-5,-1,1,5,25}

\(\Rightarrow\)y lần lượt là :-30,-10,-6,-4,20 và x lần lượt là :6,10,30,-20,4

\(=2^{10}.3^2+2^{10}-2^4.15\)

=\(2^4.\left(2^6.3^2+2^6-15\right)\)

=\(2^4.\left[2^6.\left(3^2+1\right)-15\right]\)

=\(2^4.\left(2^6.10-15\right)\)

=16.625=10000

=\(\dfrac{\left(2^2\right)^2.\left(5^2\right)^2+2^5.5^2}{2^3.5^2}\)

=\(\dfrac{2^4.5^4+2^5.5^2}{2^3.5^2}\)

=\(\dfrac{2^3.\left(2.5^4+2^2.5^2\right)}{2^3.5^2}\)

=\(\dfrac{5^2.\left(2.5^2+2^2\right)}{5^2}\)

=\(2.5^2+2^2=54\)