Question

25. the product of two natural numbers is 19. The sum of the reciprocals of their squares is

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Final Answer:

The sum of the reciprocals of the squares of the two natural numbers whose product is 19, is $1\frac{1}{361}$.

Given:

The product of two natural numbers is 19.

To Find:

The sum of the reciprocals of the squares of the two natural numbers whose product is 19, is to be determined.

Explanation:

The concepts that are important for the solution here are as follows

• The reciprocal of any natural number $n$ is $\frac{1}{n}$.
• The prime number has two factors, one factor is 1 and the other factor is the number itself.

Step 1 of 3

As per the statement given in the problem, deduce the following.

• The number 19 is a prime number.
• The factors of the prime number are 1 and 19.

Step 2 of 3

Using the information in the given problem, it is evident that the two natural numbers whose product is 19, are 1 and 19.

Their respective squares are as follows

• $1^2=1$
• $19^2=361$

So, the respective reciprocals of these squares are 1 and $\frac{1}{361}$.

Step 3 of 3

In continuation with the above, the sum of the reciprocals of their squares is

$=1+\frac{1}{361}\\\\=\frac{361+1}{361}\\\\=\frac{362}{361}\\\\=1\frac{1}{361}$

Therefore, the required correct answer is the mixed fraction $1\frac{1}{361}$.

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