SOLUTION: The sum of the reciprocal and twice the square of the reciprocal of a number is 3. Find the number(s).

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Question 413611: The sum of the reciprocal and twice the square of the reciprocal of a number is 3. Find the number(s).
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

Let x represent the number

Question states***

 1/x + 2/x^2 = 3

Solving for x

 x + 2 = 3x^2

 3x^2 - x - 2 = 0

factoring

 (3x + 2)(x-1) = 0

  (3x + 2)=0  x = -2/3

  (x-1) = 0   x = 1



CHECKING our Answer(s)***

 1 + 2 = 3

 -3/2 + 2(-3/2)^2 = -3/2 + 18/4 = -6/4 + 18/4 = 12/4 = 3 

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
 





Let  represent the number.  Then  is the reciprocal of the number and  is two times the reciprocal squared.  The sum is 3 so:











Multiply by 











Standard form:











Factor and solve the quadratic.





John



My calculator said it, I believe it, that settles it


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