Intro to Analysis: If x<y, prove x< (x+y)/2<y, and....

[jtarango]

im having trouble getting these two problems...anyone have an idea how to work em out...

1: If x<y, prove x< (x+y)/2<y

2: If 0<a<b, prove 0<a^2<b^2 and 0<a^(1/2)<b^(1/2)

 

[Loren]

Re: Intro to Analysis

If x<y, prove x< (x+y)/2<y

x<y
x+x < x+y
2x < x+y
2x/2 < (x+y)/2
x < (x+y)/2

Now, do a similar thing with the right end of the inequality, then put them together.

 

[jtarango]

Re: Intro to Analysis

thanks...that was so much more simple than what i was doing lol....i seem to over complicate things when i get frustrated...thanks again