Q: Find the rational number such that the sum of the number and its reciprocal is 13/6.

A 4/3, 3/4
B 2/3, 3/2
C 4/5, 5/4
D 9/2, 2/9
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Answer: B

Explanation:

To find the rational number such that the sum of the number and its reciprocal is 13/6, we can use the following steps:
Let the number be represented by the variable x.
Set up the equation x + (1/x) = 13/6.
Multiply both sides of the equation by x to obtain x^2 + 1 = 13/6 * x.
Simplify the right side of the equation to obtain (x^2 + 1)/x = 13/6.
Set up a quadratic equation in x by multiplying both sides of the equation by 6: 6x^2 - 13x + 6 = 0.
Rewrite the equation as (3x - 2)(2x - 3) = 0.
Solve the equation to obtain x = 2/3 or x = 3/2.
The required number is x, which is equal to 2/3 or 3/2.

Q: Find the rational number such that the sum of the number and its reciprocal is 13/6.

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