Question

The product of two natural number is 17 then the sum of reciprocal of their square is

Answer 1

Answer:

Let the numbers be X and Y.

Given,

XY = 17

Now,

Sum of reciprocals of their squares = 1/X^2 + 1/Y^2

= (x^2 + y^2)/x^2×y^2

= (x^2 + y^2)/(xy)^2

Now,

a^2 + b^2 = (a + b)^2 - 2ab

So,

= (x^2 + y^2)/(xy)^2

= [(x + y)^2 - 2xy]/ (17)^2

= (x + y)^2 - 2×17/289

= [(x + y)^2 - 34]/289

Now, put the value of (x + y) in the above expression to arrive at the answer.

Please check the question, the sum of these two numbers must be provided in the question.