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If $\mathrm{p}$ and $\mathrm{q}_{2}$ are prime numbers satisfying the condition $p^{2}-2 q^{2}=1$, then the value of $p^{2}+2 q^{2}$ is
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17
Given, $\mathrm{p}^{2}-2 \mathrm{q}^{2}=1$
Since, and are prime numbers.
Let $\mathrm{p}=3$ and $\mathrm{q}=2$
$\begin{array}{lr}\therefore \text { From Eq. (i), } & (3)^{2}-2(2)^{2}=1 \\ \Rightarrow & 9-8=1 \\ \Rightarrow & 1=1\end{array}$
Therefore, our assumption is true.
Now, $\mathrm{p}^{2}+2 \mathrm{q}^{2}=(3)^{2}+2(2)^{2}=9+8=17$
Since, and are prime numbers.
Let $\mathrm{p}=3$ and $\mathrm{q}=2$
$\begin{array}{lr}\therefore \text { From Eq. (i), } & (3)^{2}-2(2)^{2}=1 \\ \Rightarrow & 9-8=1 \\ \Rightarrow & 1=1\end{array}$
Therefore, our assumption is true.
Now, $\mathrm{p}^{2}+2 \mathrm{q}^{2}=(3)^{2}+2(2)^{2}=9+8=17$
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