The sum of a non-zero number and ten times its reciprocal is 7. Find the number.
- A4
- B3
- C5
- D6
Solution & Step-by-step Explanation
Let the non-zero number be x.
According to the problem description:
x+10×
x
1
=7
x+
x
10
=7
Multiply the entire equation by x to eliminate the fraction:
x
2
+10=7x
x
2
−7x+10=0
This is a quadratic equation. We can solve it by factoring (splitting the middle term):
x
2
−5x−2x+10=0
x(x−5)−2(x−5)=0
(x−2)(x−5)=0
This gives two possible values for x:
x=2orx=5
Among the given options, 5 is listed as option C.
According to the problem description:
x+10×
x
1
=7
x+
x
10
=7
Multiply the entire equation by x to eliminate the fraction:
x
2
+10=7x
x
2
−7x+10=0
This is a quadratic equation. We can solve it by factoring (splitting the middle term):
x
2
−5x−2x+10=0
x(x−5)−2(x−5)=0
(x−2)(x−5)=0
This gives two possible values for x:
x=2orx=5
Among the given options, 5 is listed as option C.