Question : If $y+\frac{1}{y}=3$, then what is the value of $\frac{1}{y^3}+y^3 ?$
Option 1: 12
Option 2: 27
Option 3: 24
Option 4: 18
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Correct Answer: 18
Solution :
Use: Use the following formula to solve the question:
$(y+\frac{1}{y})^3=y^3+\frac{1}{y^3}+3(y+\frac{1}{y})$
⇒ $y^3+\frac{1}{y^3}=(y+\frac{1}{y})^3-3(y+\frac{1}{y})$
⇒ $y^3+\frac{1}{y^3}=3^3-3×3$
⇒ $\frac{1}{y^3}+y^3 = 18$
Hence, the correct answer is 18.
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