Question

if a,b in R show that |a+b|=|a|+|b|

Answer 1

This statement is wrong. For example, let's a=5 and b=-5. Then both a and b are real. But

|a+b| = |5+(-5)| = |0| = 0 ≠ 10 = 5+5 = |5|+|-5| = |a|+|b|.