- #1
lovemake1
- 149
- 1
Homework Statement
la - bl <= lal + lbl
Homework Equations
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 don't feel very comfortable justifying inequalities, let alone I am 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