Question : If $(x+\frac{1}{x})=3$, then $(x^8+\frac{1}{x^8})$ is equal to:
Option 1: 2201
Option 2: 2203
Option 3: 2207
Option 4: 2213
Correct Answer: 2207
Solution :
Given: $(x+\frac{1}{x})=3$
Squaring both sides of the above equation, we get,
⇒ $(x^2+\frac{1}{x^2}+2)=9$
⇒ $x^2+\frac{1}{x^2}=7$
Again, squaring both sides of the above equation, we get,
⇒ $(x^2+\frac{1}{x^2})^2=7^2$
⇒ $x^4+\frac{1}{x^4}+2=49$
⇒ $x^4+\frac{1}{x^4}=47$
Again, squaring both sides of the above equation, we get,
⇒ $(x^4+\frac{1}{x^4})^2=47^2$
⇒ $x^8+\frac{1}{x^8}+2=2209$
⇒ $x^8+\frac{1}{x^8}=2207$
Hence, the correct answer is 2207.
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