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