Question

verify that |x+y|=|x|+|y| by taking x=1/2 and y=-1/4

Answer 1

Answer:

$lhs = |x + y| = | \frac{1}{2} + \frac{1}{4} | \\ = | \frac{3}{4} | = \sqrt{ ({ \frac{3}{4}) }^{2} } = \frac{3}{4} \: \\ rhs \: = |x | + |y| \\ = | \frac{1}{2}| + |\frac{1}{4}| \: \\ = \sqrt{( { \frac{1}{2} )}^{2} } + \sqrt{( { \frac{1}{4} )}^{2} } \\ = \frac{1}{2} + \frac{1}{4} \: \\ = \frac{3}{4} \\ therefore \: \\ lhs = rhs \\ that \: is \\ |x + y| = |x | + |y| \\ hence \: proved.$