SOLUTION: let x , y \[Element] R , prove that , 1) | x + y | = | x | + | y | \[DoubleLeftRightArrow] x . y \[GreaterEqual] 0, 2) | x - y | = | x | - | y | \[DoubleLeftRightArrow] (x - y) y \
Question 1210374: let x , y \[Element] R , prove that , 1) | x + y | = | x | + | y | \[DoubleLeftRightArrow] x . y \[GreaterEqual] 0, 2) | x - y | = | x | - | y | \[DoubleLeftRightArrow] (x - y) y \[GreaterEqual] 0, 3) | x - y | = | x | + | y | \[DoubleLeftRightArrow] x . y \[GreaterEqual] 0 Answer by ikleyn(52750) (Show Source):