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

5

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17

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Solution

The correct option is A $17$
Given $p, q$ are two prime numbers which satisfy $p^{2} - 2 q^{2} = 1$
We can see by hit and trial method that the first pair of prime number is $p = 3, q = 2$ satisfying the equation:
$3^{2} - 2 \times 2^{2} = 9 - 2 \times 4 = 9 - 8 = 1$
Value of $p^{2} + 2 q^{2} = 3^{2} + 2 \times 2^{2} = 9 + 2 \times 4 = 17$

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If p and q are prime numbers satisfying the condition p2−2q2=1, then the value of p2+2q2 is

The correct option is A 17Given p,q are two prime numbers which satisfy p2−2q2=1We can see by hit and trial method that the first pair of prime number is p=3,q=2 satisfying the equation:32−2×22=9−2×4=9−8=1Value of p2+2q2=32+2×22=9+2×4=17

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