Search any question & find its solution
Question:
Answered & Verified by Expert
- If $p$ and $q$ are prime numbers satisfying the condition $p^{2}-2 q^{2}=1$, then the value of $p^{2}+2 q^{2}$ is
Options:
Solution:
1254 Upvotes
Verified Answer
The correct answer is:
17
We have,
$$
p^{2}-2 q^{2}=1
$$
Let $p=3, q=2$
$$
\begin{array}{ll}
\text { Then, } & p^{2}-2 q^{2} \\
& =(3)^{2}-2(2)^{2}=9-8=1 \\
\therefore \quad & p^{2}-2 q^{2}=1
\end{array}
$$
Now, $p^{2}+2 q^{2}=(3)^{2}+2(2)^{2}$
$$
=9+8=17
$$
$$
p^{2}-2 q^{2}=1
$$
Let $p=3, q=2$
$$
\begin{array}{ll}
\text { Then, } & p^{2}-2 q^{2} \\
& =(3)^{2}-2(2)^{2}=9-8=1 \\
\therefore \quad & p^{2}-2 q^{2}=1
\end{array}
$$
Now, $p^{2}+2 q^{2}=(3)^{2}+2(2)^{2}$
$$
=9+8=17
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.