(A) dots, ka \(x+y=n\). Pierādīt, ka \(x^{2}+y^{2} \geq \frac{n^{2}}{2}\).

(B) dots, ka \(x+y+z=n\). Pierādīt, ka \(x^{2}+y^{2}+z^{2} \geq \frac{n^{2}}{3}\).