If a, b, x, y are positive natural numbers such that `(1)/(x) + (1)/(y) = 1` then prove that `(a^(x))/(x) + (b^(y))/(y) ge ab`.

if a,b x,y are positive natural number such that (1)/(x)+(1)/(y)=1 then (a^(x))/(x)+(a^(y))/(y)=

If a ne b and a, b, x, y are positive rational such that x+y=1 then prove that a^xb^y lt ax+by .

If x, y, z are all positive real numbers, then prove that, If x+y+z=1 , then prove that (1-x)(1-y)(1-z)ge8xyz .

Let x and y be two positive real numbers such that x+y= 1 . Then the minimum value of (1)/(x) + (1)/(y) is

Let x and y be two positive real numbers such that x + y = 1. Then the minimum value of 1/x+1/y is-

As ala2ay a, = 1 Hence (1 + al1a22" If a, b, x, y are positive natural numbers such that Consider the positive numbers a , a'"....y times and by, bo'....x ax by --+ > ab *Illustration 16. x y that-+-= 1 then prove that + x y Solution. For all these numbers, la" o'....y timel+ bbo ....x times! ya+xa" AM =

If a, b, c and x, y, z are positive, then show that (a/x + b/y + c/z) (x/a + y/b + z/c) ge 9

If y=x+(1)/(x+(1)/(x+(1)/(x+1))), prove that (dy)/(dx)=(y)/(2y-x)

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1