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The Sum of a Number and Its Reciprocal is 4.25. Find the Number. - Mathematics

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Question

The sum of a number and its reciprocal is 4.25. Find the number.

Solution

Let the numbe be x and `1/x`

For the given information

`x + 1/x = 4.25`

`(x^2 + 1)/x = 425/100 = 17/4`

`4x^2 - 17x + 4 = 0`

`4x^2 - 17x + 4 = 0`

`4x(x - 4) - 1(x - 4) = 0`

(x - 4)(4x - 1) = 0

x = 4,1/4

`x = 4 => 1/x = 1/4`

`x = 1/4 => x = 4`

Thus the number are 4 and 1/4

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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: 4 | Page no. 69
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Solution The Sum of a Number and Its Reciprocal is 4.25. Find the Number. Concept: Quadratic Equations.
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