Question

The sum of a fraction and 2 times its reciprocal is 67/21. What is the fraction?

• A.
  $\frac{5}{7}$
• B.
  $\frac{7}{3}$
• C.
  $\frac{6}{7}$
• D.
  B or C
• E.
  None of the above

Answer 1

The correct option is B

$\frac{7}{3}$
Let the fraction be = x

Then, x + $\frac{2}{x}$ = $\frac{67}{21}$ $\Rightarrow$ 21 (x${}^2$ + 2) = 67x

21 x${}^2$ - 67x + 42 = 0

$\text{x}=\frac{67\pm 31}{42}=\frac{7}{3}\text{or}\frac{6}{7}$