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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