Question 117

If $$ x + \frac{1}{x} = 99$$, find the value of $$\frac{100x}{2x^2 + 102x + 2}$$

Solution

Given : $$ x + \frac{1}{x} = 99$$

To find : $$\frac{100x}{2x^2 + 102x + 2}$$

= $$\frac{50x}{x^2 + 1 + 51x}$$

Dividing numerator and denominator by $$x$$

= $$\frac{50}{x + \frac{1}{x} + 51}$$

Substituting value of $$(x + \frac{1}{x})$$, we get :

= $$\frac{50}{99 + 51} = \frac{50}{150}$$

= $$\frac{1}{3}$$

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