plz help me sloving it
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Let n and n+2 be the integers.
Then, 1/n + 1/(n+2) = 12/35
Multiply by the LCD, 35n(n+2) to get: 35(n+2) + 35n = 12n(n+2)
70n + 70 = 12n2 + 24n
12n2 - 46n - 70 = 0
6n2 - 23n - 35 = 0
(6n + 7)(n - 5) = 0
n = -7/6 or 5
-7/6 is not an integer, so n = 5
The integers are 5 and 7.
Then, 1/n + 1/(n+2) = 12/35
Multiply by the LCD, 35n(n+2) to get: 35(n+2) + 35n = 12n(n+2)
70n + 70 = 12n2 + 24n
12n2 - 46n - 70 = 0
6n2 - 23n - 35 = 0
(6n + 7)(n - 5) = 0
n = -7/6 or 5
-7/6 is not an integer, so n = 5
The integers are 5 and 7.
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