Question 69

A number is greater than five times its reciprocal by 19/2. Find the number.

Solution

Let the number be $$x$$

According to ques,

=> $$x - (5 \times \frac{1}{x}) = \frac{19}{2}$$

=> $$\frac{x^2 - 5}{x} = \frac{19}{2}$$

=> $$2x^2 - 10 = 19x$$

=> $$2x^2 - 19x - 10 = 0$$

=> $$2x^2 + x - 20x - 10 = 0$$

=> $$x(2x + 1) - 10(2x + 1) = 0$$

=> $$(2x + 1) (x - 10) = 0$$

=> $$x = \frac{-1}{2} , 10$$

Since $$x$$ can't be negative, => $$x = 10$$

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