Suppose 3 a+3 b > =4 holds

Because 3a+3b > = 2 √ (3 AB)

Then 2 √ (3ab) > = 4,3 ab > =4, ab & gt=log3 (radix) 4, ab> 1

Because a+b= 1.

So ab < = 1/4

Assumption is not valid

So if a>0, b>0, a+b= 1, then 3 A+3 B.