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

Click here to see ALL problems on Numbers Word Problems

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