If $x_{1}, x_{2}, \ldots . x_{n}$ are any real numbers and $n$ is any positive integer, then\

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(d) : As $x_{1}, x_{2}, \ldots ., x_{n}$ are positive real numbers, we can apply $n^{	ext {th }}$ power mean theorem.\ $\frac{x_{1}^{2}+x_{2}^{2}+\ldots\left(x_{n}^{2}ight)}{n} \geq\left(\frac{x_{1}+x_{2}+x_{3}+\ldots x_{n}}{n}ight)^{2}$\ $\Rightarrow \frac{n^{2}}{n}\left(\sum_{i=1}^{n} x_{i}^{2}ight) \geq\left(\sum_{i=1}^{n} x_{i}ight)^{2}$