SOLUTION: If a number is added to its reciprocal the sum is 25/12. Find the number. (Need a complete solution Thanks)

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Question 389490: If a number is added to its reciprocal the sum is 25/12. Find the number. (Need a complete solution Thanks)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the number is n, then the
reciprocal is 1%2Fn
given:
n+%2B+1%2Fn+=+25%2F12
Multiply both sides by n
n%5E2+%2B+1+=+%2825%2F12%29%2An
12n%5E2+%2B+12+=+25n
12n%5E2+-+25n+%2B+12+=+0
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+12
b+=+-25
c+=+12
n+=+%28-%28-25%29+%2B-+sqrt%28+%28-25%29%5E2-4%2A12%2A12+%29%29%2F%282%2A12%29+
n+=+%28+25+%2B-+sqrt%28+625+-+576+%29%29%2F24+
n+=+%28+25+%2B-+sqrt%28+49+%29%29%2F24+
n+=+%2825+%2B+7%29%2F24%0D%0A%7B%7B%7Bn+=+32%2F24
n+=+4%2F3
and
n+=+%2825+-+7%29%2F24
n+=+18%2F24
n+=+3%2F4
The answer is either 3/4 or 4/3. That is because one is the reciprocal
of the other
check answer:
n%5E2+%2B+1+=+%2825%2F12%29%2An
%284%2F3%29%5E2+%2B+1+=+%2825%2F12%29%2A%284%2F3%29
16%2F9+%2B+9%2F9+=+25%2F9
25%2F9+=+25%2F9
OK