SOLUTION: The number obtained by adding the squares of a number and it's reciprocal is greater by 7/4 than the sum of the number and it's reciprocal. Find the number

Question 1066714: The number obtained by adding the squares of a number and it's reciprocal is greater by 7/4 than the sum of the number and it's reciprocal. Find the number
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I interpret the wording of your question as
find such that

Let us say that .
Then, ,
, and
.
With that, we can re-write the equation as
.
Multiplying both sides of the equal sign times , we get
,
which simplifies to

Either applying the quadratic formula, or factoring,
or "completing the square", we can find the solutions to be
and .
does not have real solutions,
but we can find real solutions for
.
Multiplying both sides of the equal sign times ,
we get the equivalent equation
<---> ,
whose solutions are
and (of course) .
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