Question

s a square minus b square is equal to 13 where A and B are natural numbers then value of a is?​

Answer 1

Answer:

a = 7

Step-by-step explanation:

Given :

a² - b² = 13,

a & b are natural numbers (a,b∈N)

Solution :

We know that,

a² - b² = (a + b)(a - b)   (Identity)

Also,

We know that, 13 is divisible by 1 & 13

⇒ 1 × 13 = 13

Since a & b are natural numbers,

⇒ (a - b) = 1

⇒ (a + b) = 13

⇒ (a + b)(a - b) = 1 × 13 = 13  (a + b) > (a - b) ⇔ 13 > 1

So,

⇒ a - b = 1 ...(i)

⇒ a + b = 13 ..(ii)

By adding both the equations,,

We get,

⇒ (a + b) + (a - b) = 13 + 1

⇒ a + b + a - b = 14

⇒ 2a = 14

⇒ a = $\frac{14}{2}$ = 7

Answer 2

answer is 7

hope it is helpful to you