If a, b, x, y are positive natural numbe...

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`.

Verified by Experts

The correct Answer is:

` :. (1) "becoms "(ya^(x)+xa^(y))/(xy) ge ab or (a^(x))/x + (a^(y))/y ge ab`

Similar Questions

Explore conceptually related problems

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

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

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

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4

If x, y, z are distinct positive numbers such that x+(1)/(y)=y+(1)/(z)=z+(1)/(x) , then the value of xyz is __________

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .

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