If 3^(x - y) = 81 and 3^(x + y) = 729 find value of x*y

Question

x, y, z and k are four non zero positive integers satisfying 1/x + y/2 = z/3 + 4/k, minimum integral value of k for integral value of x, y and z will be

Answer 1

Answer: x*y = 5 as x=5 and y = 1

3^(x-y) = 81 = 3^4 or (-3)^4
in either case
x-y = 4 -- (i)

Similarly,
3^(x+y) = 729 = 3^6 or (-3)^6
in either case

x+y = 6 - (ii)

Solving (i) and (ii)
x =5 and y =1