Question 38

Sum of twice a fraction and its reciprocal is 17/6. What is the fraction?

Solution

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

$$2 \times \frac{1}{x} + x = \frac{17}{6}$$

$$\Rightarrow (2+x^{2}) = \frac{17}{6} \times x$$

$$\Rightarrow 6x^{2}-17x+12 = 0$$

$$\Rightarrow(x-\frac{8}{6})(x-\frac{9}{6})=0$$

$$\Rightarrow x = 4/3 or 3/2$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 3/4 \text(or) 2/3$$

so the answer is option C.

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