You are Here: Home >< Maths

# Basic inequality question (analysis) watch

1. Is it true that

?

How do you prove it?

I think it's something used in solutions to a much longer question, but I'm not sure.
2. Square both sides and rearrange; if you notice that all the rearranging you do uses rather than just (since everything's nice and positive), then you're good to go.

EDIT: Shouldn't that be ? If you think of (a,b) as a point in then what the inequality is (or should be) saying is that the distance from the origin to the point (a,b) is shorter than (or equal to) the horizontal distance plus the vertical distance.
3. Well, what I'm really trying to do is to understand this:

x = (x1, x2) and a = (a1, a2)

|x1||x2 - a2| + |x1 - a1||a2| <= (|x1| + |a2|)(||x-a||)

I think what they've said is that |x1||x2 - a2| <= (|x1| + |a2|)|x2 - a2|

And |x1 ? a1||a2| <= |x1 ? a1|(|a2| + |x1|)

So |x1||x2 - a2| + |x1 - a1||a2| <= (|x2| + |a2|)(|x1 - a1| + |x2 - a2|)

But where do you get that (|x1 - a1| + |x2 - a2|) <= ||x - a||?

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 4, 2011
Today on TSR

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams