Given : $$x+\frac{1}{x}=\sqrt{13}$$
Squaring both sides
=> $$(x+\frac{1}{x})^2=(\sqrt{13})^2$$
=> $$x^2+\frac{1}{x^2}+(2.x.\frac{1}{x})=13$$
=> $$x^2+\frac{1}{x^2}=13-2=11$$ ------------(i)
Also, we know that : $$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-(2.x.\frac{1}{x})$$
Substituting value from equation (i)
=> $$(x-\frac{1}{x})^2=11-2=9$$
=> $$(x-\frac{1}{x})=\sqrt{9}=3$$
=> $$x^2-1=3x$$
=> $$\frac{3x}{x^2-1}=1$$
=> Ans - (C)
Create a FREE account and get: