Question 88

Sum of twice a fraction and 3 times its reciprocal is 29/3. What is the fraction?

Solution

Let that fraction be $$\frac{1}{x}$$

$$ 2\frac{1}{x} + 3x = \frac{29}{3}$$

$$\Rightarrow (2+3x^{2}) = \frac{19}{4} \times x$$

$$\Rightarrow 9x^{2}-29x+6 = 0$$

$$\Rightarrow(x-\frac{27}{9})(x-\frac{2}{9})=0$$

$$\Rightarrow(x-3)(x-\frac{2}{9})=0$$

$$\Rightarrow x = 3 or 2/9$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 1/3 \text(or) 9/2$$

so the answer is option D.

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