Question

Sum of a number and it's reciprocal is 19/3 what is the number

Answer 1

Step-by-step explanation:

Let the number is a .

a + 1/a = 19/3

a - 1/a = √(a + 1/a)² - 4

= √(19/3)² - 4

= √(361/9) - 4

= √(361-36)/9

= √325/9

= 5√13/ 3

2a = (19 + 5√13)/3

a = (19 + 5√13)/6

Answer 2

Let,

the number is x

The reciprocal of the number is 1/x

According to question

x+1/x = 19/3

(x^2 + 1) / x = 19/3

3x^2 - 19x + 3 = 0

Here

a = 3, b = -19 , c = 3

x = {-b ± √(b^2- 4ac)} /2a

= [19 ± √{ (-19)^2 - 4×3×2 }] / 2×3

= (19 ± 15) / 6

x= (19+15) /6 or (19-15) / 6

.... x is 17/3 or 2/3

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