Hello!!

Could you please help me with these two exercises

1.- Let be real positive numbers and

Prove that:

Hint:

2.- Let be real positive numbers and

Prove that:

Thanks a lot!!

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- April 16th 2012, 12:50 PMosodudTwo exercises about real numbers
Hello!!

Could you please help me with these two exercises

1.- Let be real positive numbers and

Prove that:

Hint:

2.- Let be real positive numbers and

Prove that:

Thanks a lot!! - April 17th 2012, 02:19 AMa tutorRe: Two exercises about real numbers
Hi. I worked from the inequality towards something I know is true and then rewrote the proof in the correct direction.

It's a bit clumsy but here's how I started.

similar for b and c.

add three of those together to get

Now add 2 to both sides and ask yourself what is another way to write etc and what is another way to write 1?

I'm a bit rushed just now.

Ask if you need more hints. - April 17th 2012, 10:02 PMosodudRe: Two exercises about real numbers
Yes. more hints please.

- April 17th 2012, 11:39 PMa tutorRe: Two exercises about real numbers

Now, using the fact that abc=1..

Now factorise the left hand side,

and then rearrange a little,

.

Nearly there...