if a,b,c,d are positive real numbers and a^2+b^2=c^2+d^2=2 then what is the max value of ac+bd?

Question

If
abcde=1 (where a,b,c,d and e are all positive real numbers)
then
what is the minimum value of a+b+c+d+e?

Answer 1

16

How:

a^2+b^2=c^2+d^2=2
From this we can say, a=b=c=d=±1
So, ac+bd = (±1)(±1)+(±1)(±1) = 1+1 = 2