Question 70

A number is greater than twice its reciprocal by 31/4. Find the number.

Solution

Let the number be $$x$$

According to ques, => $$x - \frac{2}{x} = \frac{31}{4}$$

=> $$\frac{x^2 - 2}{x} = \frac{31}{4}$$

=> $$4x^2 - 8 = 31x$$

=> $$4x^2 - 31x - 8 = 0$$

=> $$4x^2 + x - 32x - 8 = 0$$

=> $$x(4x + 1) - 8(4x + 1) = 0$$

=> $$(4x + 1)(x - 8) = 0$$

=> $$x = 8 , \frac{-1}{4}$$

=> Ans - (B)

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