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Two Natural Numbers Differ by 3. Find the Numbers, If the Sum of Their Reciprocals is 7/10. - Mathematics

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Question

Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is 7/10.

Solution

Let the numbers be x and x + 3

From the given information

`1/x + 1/(x + 3) = 7/10`

`(x + 3  + x)/(x(x + 3)) = 7/10`

`(2x + 30)/(x^2 + 3x) = 7/10`

`20x + 30 = 7x^2 + 21x`

`7x^2 + x - 30 = 0`

`7x^2 - 14x + 15x - 30 = 0`

7x(x - 2)  + 15(x - 2) = 0

(x - 2)(7x + 15) = 0

`x = 2, (-15)/7`

Since x is a natural number so x= 2

Thus the number are 2 and 5

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(A) | Q: 5 | Page no. 70
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Two Natural Numbers Differ by 3. Find the Numbers, If the Sum of Their Reciprocals is 7/10. Concept: Quadratic Equations.
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