2021 AMC 12A Question 2
AMC12 · 2021 AMC 12A
Under what conditions is $\sqrt{a^2 + b^2} = a + b$ true, where $a$ and $b$ are real numbers?
It is never true.
It is true if and only if $ab = 0.$
It is true if and only if $a + b \ge 0.$
It is true if and only if $ab = 0$ and $a +
b \ge 0.$
It is always true.