Đặt 5x=4y=2z=k suy ra \(x=\frac{k}{5};y=\frac{k}{4};z=\frac{k}{2}\)
Ta có :
x-y+z=-18
\(\frac{k}{5}-\frac{k}{4}+\frac{k}{2}=-18\)
\(k.\left(\frac{1}{5}-\frac{1}{4}+\frac{1}{2}\right)=-18\)
\(k.\frac{9}{20}=-18\)
k = -40 suy ra x = -8 ; y = -10 ; z = -20
Ta có:
\(A=\left(\frac{2}{x}+\frac{5}{y}+\frac{5}{z}\right)^{2016}=\left(\frac{2}{-8}+\frac{5}{-40}+\frac{5}{-20}\right)^{2016}=\left(\frac{5}{-8}\right)^{2016}=0\)