1) Show that for all positive reals a,b,c,d:- 1/a + 1/b + 4/c + 16/d>= 64/(a+b+c+d) 2) a,b,c are positive reals with abc=1. Prove that, 1/{a^3(b+c)} + 1/{b^3(c+a)} + 1/{c^3(a+b)}>= 3/2. 3) Solve the following inequality ...
Show that there exist infinitely many positive integers A such that (1) 2A is a perfect square ; (2) 3A is a perfect cube ; (3) 5A is a perfect fifth power. ...
