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

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Sum

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

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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

Concept: Quadratic Equations
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 6 Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6 (A) | Q 4 | Page 69
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