Question

the sum of the reciprocal of two consecutive even numbers is 7/ 24 find the numbers​

Answer 1

Answer:

Let smaller even integer = x

Then larger even integer = x + 2

"Reciprocal of" means "1 over"

1 1 7

--- + ----- = ----

x x+2 24

The LCD is 24x(x+2). Multiply through by that LCD

1 1 7

24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·----

x x+2 24

Cancel what will cancel

1 1 7

24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·----

x x+2 24

24(x+2) + 24x = x(x+2)·7

24x + 48 + 24x = (x²+2x)7

48x + 48 = 7x² + 14x

0 = 7x² - 34x - 48

0 = (7x + 8)(x - 6)

Set first factor = 0

7x + 8 = 0

7x = -8

x = -8/7

Set second factor = 0

x - 6 = 0

x = 6

Discard fraction answer. Solution: smaller = 6, larger = 6+2 or 8