Expert: Paul Klarreich - 3/29/2009

Question
Hello! I've the following problem: x, y are positive numbers and x+y=1. How can i proof, this inequality  x*y^(2/3)<7/3 ?

thanks

Answer
Questioner:   grull
Country:  Hungary
Category:  Advanced Math
Private:  Yes
 
Subject:  inequality
Question:  Hello! I've the following problem: x, y are positive numbers and x+y=1. How can i proof, this inequality  x*y^(2/3)<7/3 ?

thanks


If  y = 1 - x,  then  x  is in (0,1), because you said both x and y are positive.

Did you mean:  

x(y^(2/3)) < 7/3  (A)

or

(xy)^(2/3) < 7/3  (B)

In either case, your problem is not very interesting, because:

abs(y) < 1, and abs(x) < 1

y^(2/3) < 1^(2/3) = 1

So x(y^(2/3)) < 1 * 1 = 1 < 7/3

(xy)^(2/3) < (1*1)^2/3 = 1 < 7/3

maybe you mistyped.