Question

A number added to its reciprocal is 4.25 find the number

Answer 1

Let The Number be x
According to Given Question
1 + x = 4.25
--
 x

1 + x²   = 425
--------     -------
     x         100
100 + 100x² = 425x
100x² - 425x + 100 = 0
Dividing the Equation by 25

4x² - 17x + 4 = 0
4x² - 16x - x + 4 = 0
4x(x - 4) -1(x - 4) = 0
(4x - 1)(x - 4) = 0
x = 1/4 OR x = 4
So the Number is either 1/4 or 4

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Answer 2

Let the number be x then its reciprocal is (1/x).

Number added to its reciprocal is 4.25
So,  x + (1/x)               = 4.25
⇒ x2 + 1                     = (425/100)x
⇒ x2 + 1                     = (17/4)x
⇒ 4x2 + 4                    = 17x
⇒ 4x2 – 17x + 4          = 0
⇒ 4x2 – 16x – x + 4     = 0
⇒ 4x(x – 4) – 1( x – 4)  = 0
⇒ (x – 4)(4x  – 1)          = 0
⇒ (x – 4) = 0 or (4x  – 1) = 0
∴ x = 4 or (1/4)
Thus the number is 4 or (1/4).