The sum of a non-zero number and twice its reciprocal is
4
33
​
. Find the number.

Let the non-zero number be x.
According to the problem statement:

x+2(
x
1
​
)=
4
33
​

x+
x
2
​
=
4
33
​

x
x
2
+2
​
=
4
33
​

Cross-multiplying gives:

4(x
2
+2)=33x
4x
2
+8=33x
4x
2
−33x+8=0
Splitting the middle term to factorise:

4x
2
−32x−x+8=0
4x(x−8)−1(x−8)=0
(4x−1)(x−8)=0
This gives two possible values:

x=8orx=
4
1
​

Among the given options, 8 is listed.