If (a+b)/2 = rad(ab), which of the following can be true

I a>0
II a=0
III a<0

I picked I II and III but apparently its only I and II

If a < 0, then you’ve got trouble. If b is positive, then \sqrt{ab} will be the square root of a negative number, which is a no-no. If b is also negative, though, which would make the number inside the square root positive, then you’ve got a negative on the left side of the equation. You don’t take the square root of a positive number and get a negative.

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