SOLUTION: typo in the last one its actually the sume of an integer and its reciprocal is 65/8. Find the integer

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Question 371970: typo in the last one its actually
the sume of an integer and its reciprocal is 65/8. Find the integer
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N%2B1%2FN=65%2F8
Multiuply both sides by 8N
8N%5E2%2B8=65N
8N%5E2-65N%2B8=0
%288N-1%29%28N-8%29=0
Two solutions but only one is an integer solution.
N-8=0
highlight%28N=8%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!



Hi,

Let x represent the integer

question states

x + 1/x = 65/8    Multiplying each term by 8x so as all denominators = 1

8x^2 + 8 = 65x

8x^2 - 65x + 8 = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2865+%2B-+sqrt%28+3969+%29%29%2F%2816%29+

x+=+%2865+%2B-+63%29%2F%2816%29+

x = 2/16  cannot use (not an integer)

x = 128/16

x = 8

checking our answer

8 + 1/8 = 64/8 + 1/8 = 65/8