Question

The sum of two numbers is 7 and the difference of their reciprocals is 1/12
What are the two numbers ?​

Answer 1

Step-by-step explanation:

x + y = 7

y = 7 - x ___________(1)

1/x - 1/y = 1/12

y - x / xy = 1/12

12x - 12y = xy ___________(2)

substituting 1 eq in 2nd

12x - 12 (7-x) = (7-x)x

12x - 84 - 12x = 7x - x^2

84 = 7x - x^2

x^2 - 7x + 84 = 0

solving by formula

d= b^2 - 4ac

d = 49 - 336

d = - 297

x = -b √ d / 2a

x = 7 √ -297 /2

hence no real roots

good day