Question 46

The sum of thrice a number and twice its reciprocal is 97/4. What is the number?

Solution

Let the number be $$x$$

According to ques, => $$(3x + \frac{2}{x}) = \frac{97}{4}$$

=> $$\frac{3x^2 + 2}{x} = \frac{97}{4}$$

=> $$12x^2 + 8 = 97x$$

=> $$12x^2 - 97x + 8 = 0$$

=> $$12x^2 - 96x - x + 8 = 0$$

=> $$12x(x - 8) - 1(x - 8) = 0$$

=> $$(12x - 1) (x - 8) = 0$$

=> $$x = \frac{1}{12} , 8$$

$$\therefore$$ The number is 8

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