Question

I am asked to show that if a and b are of the same sign that the absolute value of their sum is equal to the sum of their absolute values. I have a feeling that it is related to the use of the \sqrt{x^2} function but have been unable to figure out the relationship. How would I proceed showing this relationship?

Answer 1

go with the definition of \(|x|\)

Answer 2

if \(x>0\) then \(|x|=x\) and if \(x<0\) then \(|x|=-x\)

Answer 3

ignore \(\sqrt{x^2}\) that just complicates things

Answer 4

so for example, if \(a>0,b>0\) then \(|a|=a\) and \(|b|=b\) and so \(|a|+|b|=a+b\)

Answer 5

How would that relate to showing \[|a| + |b| = |a + b|\] ?