Question

If p+p! =p^2 then p=​

Answer 1

Required Answer:-

Given:

• p + p! = p²

To find:

• The values of p.

Solution:

We have,

➡ p + p! = p²

Note that,

➡ Factorial of a positive integer is the product of all the numbers from 1 to n. For example, factorial of 5 is = 5 × 4 × 3 × 2 × 1 = 120 etc.

Factorial of n = n × (n - 1) × (n - 2) × ...1

= n × (n - 1)!

So, we can write that,

➡ p + p × (p - 1)! = p²

Taking p as common,

➡ p × [1 + (p - 1)!] = p²

➡ 1 + (p - 1)! = p

➡ p - (p - 1)! = 1 — (i)

By trial and error method, we found that equation (i) is true when p = 2 i.e,

2 - 1! = 2 - 1 = 1 which is true.

★ So, p = 2 is a solution to this question.

Again, we also found that, when p = 3,

p - (p - 1)!

= 3 - 2!

= 3 - 2

= 1 which is also true.

★ Hence, the values of p are 2 and 3.

Answer:

• The values of p are 2 and 3.