Question : If $x^2+\frac{1}{x^2}=66$, the value of $x-\frac{1}{x}$ is:
Option 1: 10
Option 2: 8
Option 3: 9
Option 4: 6
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Answer (1)
23rd Jan, 2024
Correct Answer: 8
Solution :
Given, $x^2+\frac{1}{x^2}=66$
⇒ $x^2+\frac{1}{x^2} -2=66-2$
⇒ $x^2+\frac{1}{x^2} -2(x)(\frac{1}{x})=64$
We know that $(a-b)^2 = a^2+b^2-2ab$
So, $(x-\frac{1}{x})^2=8^2$
⇒ $(x-\frac{1}{x})=8$
Hence, the correct answer is 8.
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