COMEDK · Maths · 1. Basic of Mathematics
- 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
- A 5
- B 15
- C 16
- D 17
Answer & Solution
Correct Answer
(D) 17
Step-by-step Solution
Detailed explanation
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, \(p^{2}+2 q^{2}=(3)^{2}+2(2)^{2}\) \[ =9+8=17 \]
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