Question : If $(y-\frac{1}{y})=8$, find the value of $(y^2+\frac{1}{y^2})$.
Option 1: 64
Option 2: 62
Option 3: 60
Option 4: 66
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Correct Answer: 66
Solution :
Given, $(y-\frac{1}{y})=8$
Squaring both sides, we get:
$y^2+\frac{1}{y^2}-2(y)(\frac{1}{y})=64$
⇒ $y^2+\frac{1}{y^2}=64+2$
⇒ $y^2+\frac{1}{y^2}=66$
Hence, the correct answer is 66.
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