Answer to Question #3400 in Real Analysis for junel
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
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.