I have to prove that x<(x+y)/2<y and x<y can any one help me?
also I am having problems with if x is less then or equal to 0
y is less then or equal to 0
then prove (xy)^1/2 less then or equal to x+y/2
I have to prove that x<(x+y)/2<y and x<y can any one help me?
We know that,
x=x
Now I am going to add "x" to the left side.
And "y" to the right side.
But y>x.
Thus,
x+x<x+y
2x<x+y
Thus, (divide by 2 which is a positive number),
x<(x+y)/2
The case,
(x+y)/2<y
I leave to you to prove.
(Hint: It is similar to how I did it)