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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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