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## Homework Statement

Let a & b be real numbers.

Prove that:

|a+b|<=|a|+|b|

## Homework Equations

|x|=[tex]\sqrt{x^{2}}[/tex]

## The Attempt at a Solution

|a+b|

=[tex]\sqrt{(a+b)^{2}}[/tex]

=[tex]\sqrt{(a^{2}+2ab+b^{2})}[/tex] <= [tex]\sqrt{a^{2}} + [tex]\sqrt{b^{2}}[/tex]

|a|=[tex]\sqrt{a^{2}}[/tex]

|b|=[tex]\sqrt{b^{2}}[/tex]

I feel like this is lacking in foundation, but I lack in the foundation of proofs involving absolute value. Thanks in advance for the assistance.

Joe

Sorry for the ugly formatting, tex is cumbersome sometimes.

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