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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