ab=81, a=81/b
s=a+b using a from above in this we get:
s(b)=81/b +b
s(b)=(81+b^2)/b
ds/db=(2b*b-81-b^2)/b^2
ds/db=(2b^2-81-b^2)/b^2
ds/db=(b^2-81)/b^2
d2s/db2=(2b^3-2b^3+81)/b^4
d2s/db2=81/b^4 since b is positive we know that the acceleration is positive so that when ds/db=0 it is a minimum for s(b)
ds/db=0 only when b^2-81=0, b^2=81, b=9
The two positive numbers are 9 and 9.