Question

If p and q are prime numbers, such that the numbers p + q and p + 7q are both perfect squares, the value of p is

Answer 1

Answer:

p = 2

Step-by-step explanation:

Let p + q = a²   -------- [1]

     p + 7q = b² ---------[2]

subtracting [1] from [2]

6q = b² - a² = (b + a)(b - a).

Thus one of b ± a must be even.

But since their difference is even i.e. b²- a² = 6q, both are even.

Since q is prime, we must have q = 2, then b = 4, a = 2, and p = 2.

Answer 2

Answer:

Step-by-step explanation:

easy explanation : see the options put p = 2  

now the sum of two prime numbers is a perfect square  let's take q also equal to 2  

hence  

2+2 = 4  

and  

2 + 7(2) = 14+2 = 16 is also a perfect square

hence the numbers p and q both are equal and are 2 'option 1 is the answer'