Question

If a and b are positive real numbers such that a^3 + b^3 = 126 and ab is an integer, what is the maximum possible value of ab?

Answer 1

Hi Mate !!!!

We know that A.M _> G.M

A.M = a³ + b³ / 2. and. G.M = ( ab )^ ( 1 / (2 / 3 ))

..............................................................................

=> ( ab ) ^ ( 3 / 2 ) _< 61

=>. ab _< ( 61 )^ ( 2 / 3 )

So, maximum value of ab is ( 3721 ) ^(1/3)

_< denotes less or equal to