Question
Download Solution PDFIf \(y + {{1} \over y} = 3\), then what is the value of \({{1} \over y^3} + y^3 + 2 \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(y + {{1} \over y} = 3\)
Concept used:
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
\(y + {{1} \over y} = 3\)
⇒ \((y + {{1} \over y})^3 = 27\)
⇒ \(y^3 + {{1} \over y}^3 +3(y +\frac{1}{y})= 27\)
⇒ \(y^3 + {{1} \over y}^3 +3 \times 3= 27\)
⇒ \(y^3 + {{1} \over y}^3 +9= 27\)
⇒ \(y^3 + {{1} \over y}^3= 18\)
⇒ \({{1} \over y^3} + y^3 + 2 \) = 20
∴ The required answer is 20.
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