 # a+b=1a and b are positive real nos.Prove that: (a^a)(b^b)+(a^b)(b^a)>1. 10 years ago

Dear Pratik,

Given that a + b = 1.

That is We need to prove that Now substitute in the expression :

Thus, Observe the above expression.

Since and b are positivie real numbers less than 1, the product Now let us observe the term in the square bracket.

Since is negative.

Thus, the power of the first term is negative and hence the first term, that is, Similaraly, the power of the second term is negative and hence the second term, that is Thus, the sum of two numbers which are less than 1 is also less than 1.

That is the term inside the square bracket, Thus, the product, Thus, the expression, and it is equal to 1 if Therefore, we have Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums.