If $$x + \frac{1}{x} = 99{\text{,}}$$ find the value of $$\frac{{100x}}{{2{x^2} + 2 + 102x}}$$ is?
A. $$\frac{1}{6}$$
B. $$\frac{1}{2}$$
C. $$\frac{1}{3}$$
D. $$\frac{1}{4}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & x + \frac{1}{x} = 99 \cr & \therefore {x^2} + 1 = 99x \cr & \Rightarrow 2\left( {{x^2} + 1} \right) = 2 \times 99x \cr & \Rightarrow 2{x^2} + 2 = 198x \cr & = \frac{{100x}}{{2{x^2} + 2 + 102x}} \cr & = {\text{ }}\frac{{100x}}{{198x + 102x}} \cr & = \frac{{100x}}{{300x}} \cr & = \frac{1}{3} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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