SOLUTION: The sum of a number and twice its reciprocal is 51/5. What is the number?

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Question 1190827: The sum of a number and twice its reciprocal is 51/5. What is the number?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the number be x; then twice the reciprocal is 2/x.

The sum of the two s 51/5:

x%2B2%2Fx=51%2F5

Multiply everything by the least common denominator 5x to clear fractions:

5x%5E2%2B10=51x
5x%5E2-51x%2B10=0
%285x-1%29%28x-10%29=0
x=1%2F5 or x=10

ANSWER: The two numbers are 1/5 and 10

CHECK:
x=1/5 --> 2/x=10 --> x+2/x=10+1/5=51/5
x=10 --> 2/x=1/5 --> x+2/x=10+1/5=51/5