Question

If $p$ and $q$ are prime numbers satisfying the condition $p^2-2q^2=1$, then the value of $p^2+2q^2$ is

• A. $5$
• B. $15$
• C. $16$
• D. $17$

Answer 1

The correct option is D

$17$

Step-1:Check the condition

Given $p$ and $q$ are prime numbers and also satisfying the given condition $p^2-2q^2=1$ -------(i)

Take the first two prime numbers$2$, $3$

Let us assume $p=3$ and $q=2$

Substitute the values of $p$ and $q$ in the L.H.S of equation (i)

$\begin{array}{c}\text{∴L.H.S}=p^2-2q^2\\ ={\left(3\right)}^2-2\times {\left(2\right)}^2\\ =9-8\\ =1\left(\text{R.H.S}\right)\end{array}$

The prime numbers satisfy the given condition $p^2-2q^2=1$

Step 2: Find the value of $p^2+2q^2$

Take the values of $p=3$ and $q=2$

Substitute in $p^2+2q^2$

$\begin{array}{rcl}\therefore p^2+q^2& =& {\left(3\right)}^2+2{\left(2\right)}^2\\ & =& 17\end{array}$

Hence the value of $p^2+2q^2$= $17$