Show that if a and b are real numbers, then a+b = 0 if and only if both a and b are zero (Clue: Assume that a + b = 0. If b is not zero, we can write = a/b, and squaring both sides, we find 1 = a²/b². The right hand side is positive, since both a² and b² are positive (they are squares). But the left hand side is negative. Because of this contradiction, b must be zero. As before, we find that a is also zero.