Question

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

Answer 1

Answer:

Step-by-step explanation:

Let the number be 'x'

Reciprocal = $\frac{1}{x}$

$x+\frac{1}{x}=\frac{5}{2}\\\\\frac{x*x}{1*x}+\frac{1}{x}=\frac{5}{2}\\\\\frac{x^{2}+1}{x}=\frac{5}{2}$

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