Answer:
Step-by-step explanation:
Let the number be 'x'
Reciprocal = [tex]\frac{1}{x}[/tex]
[tex]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}[/tex]
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
