Answer to Question #3400 in Real Analysis for junel

Question

If a,b ϵ R, show that a[sup]2[/sup] + b[sup]2[/sup] = 0, if and only if a = 0 and b = 0

Answer 1

For any n n² >=0.
Thus the sum of two positive numbers is always greater or equal to zero.
If a > 0 and b = 0 then a² + 0² > 0, analogously for b > 0 and a = 0. Thus we see to satisfy the expression a² + b² = 0, a and b must be equal to zero at the same time.