The reciprocal of two less than a certain number is twice the reciprocal of the number itself. What is the number?

Number is 4

Step-by-step explanation:

Given:  reciprocal of two less than a certain number is twice the reciprocal of the number itself

To find: The number

Solution:

Let the number be x

Reciprocal of two less than a certain number =

Reciprocal of the number itself =

According to question,

So, number is 4

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4