Question : 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 $P$?
Option 1: $287\pi$
Option 2: $547\pi$
Option 3: $574\pi$
Option 4: $278\pi$
Correct Answer: $574\pi$
Solution :
Given: $\frac{1}{x}+x=17$
Squaring both sides, we have,
⇒ $(\frac{1}{x}+x)^{2}=17^{2}$
⇒ $\frac{1}{x^{2}}+x^{2}+2=289$
⇒ $\frac{1}{x^{2}}+x^{2}=287$
Circumference of circle $P$ = $2\pi r$
= $2×\pi ×287$
= $574\pi $
Hence, the correct answer is $574\pi $.
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