Question

The sum of two numbers is 13 and the sum of their reciprocals is 13/40. Calculate the numbers.​

Answer 1

Step-by-step explanation:

let the numbers be x and y

given that

x+y=13

and

1/x+ 1/y=13/40

from 1st equation we get x = 13-y put it in the second equation and solve

Answer 2

Step-by-step explanation:

Let the numbers be x and y.

According to the question,

x+y=13

x=13-y ---------(i)

and

$\frac{1}{x} + \frac{1}{y} = \frac{13}{40}$

$\frac{y + x}{xy} = \frac{13}{40}$

$40y + 40x = 13xy$

40y+40(13-y) = 13y(13-y)

40y+520-40y = 169y-13y²

13y²-169y+520=0

y²-13y+40=0

y²-5y-8y+40=0

y(y-5)-8(y-5)=0

(y-8)(y-5)=0

y=8 or y=5

If y=8,

x=13-8

x=5

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