Question 138
Let $x$, $y$, and $z$ be real numbers.
a. Prove that
$$
x + y \gt |x - y|
$$
if and only if $x$ and $y$ are both positive.
b. Find an inequality involving the variables $x$, $y$, and $z$, using only the operations of addition, subtraction, multiplication and absolute value, that is true if and only if $x$, $y$, and $z$ are all positive.
a. Prove that
$$
x + y \gt |x - y|
$$
if and only if $x$ and $y$ are both positive.
b. Find an inequality involving the variables $x$, $y$, and $z$, using only the operations of addition, subtraction, multiplication and absolute value, that is true if and only if $x$, $y$, and $z$ are all positive.