J jtarango New member Joined Feb 4, 2008 Messages 3 Feb 4, 2008 #1 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)
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)
L Loren Senior Member Joined Aug 28, 2007 Messages 1,298 Feb 4, 2008 #2 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.
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.
J jtarango New member Joined Feb 4, 2008 Messages 3 Feb 4, 2008 #3 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
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
