SOLUTION: The sum of a number, its reciprocal and 4 times its reciprocal is 6. What is a possible number? A) 1 B) 4 C) 6 D) -3 E) -1

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Question 281883: The sum of a number, its reciprocal and 4 times its reciprocal is 6. What is a possible number?
A) 1 B) 4 C) 6 D) -3 E) -1

Found 2 solutions by J2R2R, Greenfinch:
Answer by J2R2R(94) About Me  (Show Source):
You can put this solution on YOUR website!
The most obvious answer I try when seeing questions like this is 1 since 1 and its reciprocal 1/1 is also 1 and adding the reciprocal any number of times will always give another whole number. There are others but they are not so obvious.

So let us take you to the solution.
Suppose the number is x

Then x + 1/x + 4/x = 6
x + 5/x = 6
x^2 + 5 = 6x

Giving
x^2 - 6x + 5 = 0
(x - 5)(x - 1) = 0
x - 5 = 0 and x - 1 = 0 as solutions

So we have x = 1 and x = 5

Check:
1 + 1/1 + 4/1 = 6
5 + 1/5 + 4/5 = 6
The answer 5 wasn’t given in the options for your answer.

Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
X + 1/X + 4/X = 6 multiply by X
x^2 + 5 = 6X
x^2 - 6x + 5 = 0
(X - 5)(X - 1)=0
X = 1 or 5
So A fits