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

The reciprocal of a number is 1/the number.
Assume that the number is y

Now, we will translate the English wordings of the problem into an equation as follows:
y + (1/y) = 4 x (1/y)    (multiply both sides by y to eliminate the denominators)
y^2 + 1 = 4
y^2 = 4-1 = 3
y = +/- sqrt(3) = +/- 1.732

Based on this,
either the number is 1.732
or the number is -1.732

The answer is