(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

la - bl <= lal + lbl

2. Relevant equations

3. The attempt at a solution

I have prooved this triangle inequality. but please check if there are any obvious errors.

-2ab <= 2labl

a^2 - 2ab + b^2 <= a^2 + 2labl + b^2

( la - bl)^2 <= (lal + lbl)^2

*sqrt both sides

la - bl <= lal + lbl

The problem is now that i have somewhat prooved this inequality, how do i justify it?

In an assignment or on a test I need to write the process of my work.

How would i go aobut justifying this proof?

Heres my shot at it:

ab <= l ab l is true for all real numbers

therefore -2ab <= 2l ab l is the same case.

add a^2, b^2 to both sides and squareroot it.

lal >= a

lbl >= b

therefore lal + lbl >= la - bl

I dont feel very comfortable justifying inequalities, let alone im not very good at it.

are there any ways to justify without feeling too awkard? some keywords i need to be using?

please help, i want to learn more

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# Homework Help: How to justify?

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