The sum of a rational number and its reciprocal is 13/6.
The sum of a rational number and its reciprocal is 13/6. Find the number.
Answer/Solution
2/3 or 3/2
Steps/Work
Let the number be x.
Then, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x2 – 13x + 6 = 0
=> 6x2 – 9x – 4x + 6 = 0 => (3x – 2) (2x – 3) = 0
x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.
Answer is D.
Then, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x2 – 13x + 6 = 0
=> 6x2 – 9x – 4x + 6 = 0 => (3x – 2) (2x – 3) = 0
x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.
Answer is D.