SOLUTION: The sum of a number and its reciprocal is 25/12. What is the number?

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Question 24958: The sum of a number and its reciprocal is 25/12. What is the number?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the required number. You can write:
n+%2B+1%2Fn+=+25%2F12 Simplify and solve for n.
%28n%5E2+%2B+1%29%2Fn+=+25%2F12 Multiply both sides of the equation by n.
n%5E2+%2B+1+=+25n%2F12 Multiply both sides by 12 and simplify.
12n%5E2+%2B+12+=+25n Subtract 25n from both sides.
12n%5E2+-+25n+%2B+12+=+0 Solve for n by factoring.
%283n+-+4%29%284n+-+3%29+=+0 Apply the zero products principle.
3n+-+4+=+0 and/or 4n+-+3+=+0
If 3n+-+4+=+0 then 3n+=+4 and n+=+4%2F3
If 4n+-+3+=+0 then 4n+=+3 and n+=+3%2F4
The answer is: There are two numbers that fit this situation.
4%2F3 and 3%2F4 Check:
4%2F3+%2B+3%2F4+=+%2816+%2B+9%29%2F12 = 25%2F12
3%2F4+%2B+4%2F3+=+%289+%2B+16%29%2F12 = 25%2F12