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)x=−√3 orx=sqrt(3)x=√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+1x=4×1x
:. 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