Question
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers.
algebraic expression is:
1/n-2 + (2)1/n = 5/12
algebraic expression is:
1/n-2 + (2)1/n = 5/12
Answers
Damon
small = s and b = big
s = b-2
1/s + 2/b = 5/12
so
1/(b-2) + 2/b = 5/12 agreed
multiply by 12 b (b-2)
12 b + 24(b-2) = 5 b(b-2)
12 b + 24 b - 48 = 5 b^2 - 10 b
0 = 5 b^2 - 46 b + 48
0 = (b-8)(5b-6)
so use b = 8
s = b-2 = 6
s = b-2
1/s + 2/b = 5/12
so
1/(b-2) + 2/b = 5/12 agreed
multiply by 12 b (b-2)
12 b + 24(b-2) = 5 b(b-2)
12 b + 24 b - 48 = 5 b^2 - 10 b
0 = 5 b^2 - 46 b + 48
0 = (b-8)(5b-6)
so use b = 8
s = b-2 = 6