KCET · Maths · Basic of Mathematics
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
- A 5
- B 15
- C 16
- D 17
Answer & Solution
Correct Answer
(D) 17
Step-by-step Solution
Detailed explanation
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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