Question

((a-2)+(2+i))+((b-2))+(2-i))=-i if a and b are real numbers then which of the following are the correct values of a and b? ​

Answer 1

If a and b are positive real numbers, then a+b≥2ab−−√.

I know how to do the direct proof, but in this case, I want to try proving it by contradiction. I have tried manipulating the inequality a+b<2ab−−√ after making the assumption that a,b>0 to get a contadiction a,b≤0.

a+ba2−2ab+b2(a−b)2<2ab−−√<0<0

How do I show that a,b≤0?