Question

The sum of a number and its reciprocal is 5/2 Find the number and its reciprocal.

Answer 1

Explanation:

Let the number be 'x'

Reciprocal =
`(1)/(x)`

`x+(1)/(x)=(5)/(2)\\\\(x*x)/(1*x)+(1)/(x)=(5)/(2)\\\\(x^(2)+1)/(x)=(5)/(2)`

Cross multiply

(x² + 1) *2 = 5*x

2x² + 2 = 5x

2x² - 5x + 2 =0

Factorize the equation,

Sum = -5

Product = 4

Factors = -1 , -4

2x² - x - 4x + 2 = 0

x(2x - 1) - 2(2x - 1) = 0

(2x -1 )(x - 2) = 0

2x - 1 = 0 ; x -2 = 0

2x =1 ; x = 2

x = 1/2

Number = 2 , and its reciprocal = 1/2