SOLUTION: Solve and verify your answer. The sum of a number and its reciprocal is 13 / 6. Find the numbers.

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Question 1130449: Solve and verify your answer.
The sum of a number and its reciprocal is 13 / 6. Find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let a number be x and its reciprocal 1%2Fx

if the sum of a number and its reciprocal is 13+%2F+6, we have
x%2B1%2Fx=13%2F6
%28x%5E2%2B1%29%2Fx=13%2F6...........cross multiply
6%28x%5E2%2B1%29=13x
6x%5E2%2B6=13x
6x%5E2-4x-9x%2B6=0
%286x%5E2-4x%29-%289x-6%29=0
2x%283x-2%29-3%283x-2%29=0
%282x+-+3%29+%283x+-+2%29+=+0
solutions:

if %282x+-+3%29+=+0=>2x=3=>x=3%2F2
if +%283x+-+2%29+=+0=>3x=2=>x=2%2F3

so, your numbers are:
x=3%2F2 and its reciprocal x=2%2F3
or vice versa
x=2%2F3 and its reciprocal x=3%2F2