Question

An integer minus 5 times its reciprocal is
76
9
What is the integer?

Answer 1

Answer: The only one of these that's an integer is 9.

Explanation: Let X be the integer. Then

X - 3/X = 26/3. Multiplying by 3X on both sides:

3X^2 - 9 = 26X

3X^2 - 26X - 9 = 0

X = (26 +/- SQRT(26^2-(4*(-27))))/6 = (26 +/- 28) / 6,

so the two solutions for X are 1/3 and 54/6 = 9.