Question

Help please:
If a and b are +ve real numbers such that a+b=1,prove A^ab^b + a^bb^a ≤ 1

Answer 1

Do you mean this for the second equation? \[a^a*b^b+a^b*b^a \le1\]

Answer 2

yes, u r right...thanks

Answer 3

b=1-a
so f(a)=a^a(1-a)^1-a+a^(1-a) (1-a)^a

Answer 4

are you sure it is right?

Answer 5

mahmit yes...thanks

Answer 6

it is an olympiad question

Answer 7

find f(0+)=f(1-) then show it is 1 and both are corner maximum value.