Question 117

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

Solution

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

$$x^{2}+1=99x$$

multiply with 2 on both sides

$$2x^{2}+2=198x$$

add 102x on both sides,

$$2x^{2}+2+102x=198x+102x$$

$$2x^{2}+2+102x=300x$$

$$2x^{2}+2+102x=3\times100x$$

$$\frac{2x^{2}+102x+2}{100x}=3$$

$$\frac{100x}{2x^{2}+102x+2}=\frac{1}{3}$$

so the answer is option C.

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