# The sum of a number and its reciprocal is equal to 4 times the reciprocal, What is the number?

##### 3 Answers

There are two possibilities:

# x=-sqrt(3)# or#x=sqrt(3)#

#### Explanation:

Suppose the number is

Then the "reciprocal" of this number is

We are told that:

"The sum of a number and its reciprocal is equal to 4 times the reciprocal"

Therefore:

# x + 1/x = 4 xx 1/x #

# :. x = 4 xx 1/x - 1 xx 1/x#

# :. x = 3 xx 1/x #

# :. x^2 = 3 #

# :. x = +-sqrt(3 ) #

on the left side, multiply n by

giving:

so...

...check your work, when you can:

(the same sequence also applies for the

I got two possible numbers:

#### Explanation:

Let us call the unknown number

rearrange:

(with