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The product of tow natural numbers is 17. what is the sum of the squares of their reciprocals?

Question

The product of tow natural numbers is 17. what is the sum of the squares of their reciprocals?

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Solution 1

The product of two natural numbers is 17. This means that the two numbers are 1 and 17 because 17 is a prime number and can only be divided evenly by 1 and itself.

The reciprocal of a number is 1 divided by that number. So, the reciprocals of 1 and 17 are 1/1 = 1 and 1/17.

The square of a number is that number multiplied by itself. So, the squares of the reciprocals are 11 = 1 and (1/17)(1/17) = 1/289.

The sum of these squares is 1 + 1/289 = 289/289 + 1/289 = 290/289 = 1.0034602076124567.

This problem has been solved

Solution 2

The product of two natural numbers is 17. This means that the two numbers are 1 and 17 because 17 is a prime number and can only be divided evenly by 1 and itself.

The reciprocal of a number is 1 divided by that number. So, the reciprocals of 1 and 17 are 1/1 = 1 and 1/17.

The square of a number is that number multiplied by itself. So, the squares of the reciprocals are 11 = 1 and (1/17)(1/17) = 1/289.

The sum of these squares is 1 + 1/289 = 289/289 + 1/289 = 290/289 = 1.0034602076124567.

This problem has been solved

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