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put this solution on YOUR website! The sum of the reciprocals of two consecutive even numbers is 7/24.
Find the numbers.
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
Edwin
AnlytcPhil@aol.com
