PVT Test PDF

$ \begin{aligned}
&\text { Ex. } 7 . \text { Evaluate }:(313 \times 313+287 \times 287)\\
&\begin{aligned}
&\text { Sol. } \quad\left(a^{2}+b^{2}\right)=\frac{1}{2}\left[(a+b)^{2}+(a-b)^{2}\right] \\
&\therefore \quad(313)^{2}+(287)^{2}=\frac{1}{2}\left[(313+287)^{2}+(313-287)^{2}\right]=\frac{1}{2}\left[(600)^{2}+(26)^{2}\right] \\
&\quad=\frac{1}{2}(360000+676)=180338 .
\end{aligned}
\end{aligned}$