Question 119

If $$\frac{1}{x^{2}}+x^{2}$$ represents the radius of circle P and $$\ \frac{1}{x}+x=17$$, which of the following best approximates the circumference of circle P ?

Solution

Given : $$\ \frac{1}{x}+x=17$$

Squaring both sides,

=> $$(\frac{1}{x}+x)^2=(17)^2$$

=> $$x^2+\frac{1}{x^2}+2=289$$

=> $$x^2+\frac{1}{x^2}=289-2=287$$

=> Radius of circle = $$r=287$$

$$\therefore$$ Circumference = $$2\pi r$$

= $$2\times\pi\times287=574\pi$$

=> Ans - (C)

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