Question : If $(x^2-2x+1)=0$, then the value of $x^4+\frac{1}{x^4}$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
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Correct Answer: 2
Solution :
Given: $(x^2-2x+1)=0$
⇒ $x^2+1=2x$
Divide the given equation by $x$ on both sides, we get,
⇒ $x+\frac{1}{x}=2$
On squaring the above equation on both sides, we get,
⇒ $x^2+\frac{1}{x^2}+2=4$
⇒ $x^2+\frac{1}{x^2}=2$
On squaring the above equation on both sides, we get,
⇒ $(x^2+\frac{1}{x^2})^2=2^2$
⇒ $(x^4+\frac{1}{x^4})+2=4$
⇒ $(x^4+\frac{1}{x^4})=2$
Hence, the correct answer is 2.
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