Question
Download Solution PDFIf \(\rm K+\frac{1}{K}=3\), then what is the value of \(\frac{1}{K^3}+K^3\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm K+\frac{1}{K}=3\)
Concept used:
If \(\rm a+\frac{1}{a}=b\)
Then,
\(a^3+\frac{1}{a^3} = b^3 - 3b\)
Calculation:
\(\frac{1}{K^3}+K^3\)
⇒ \((\rm K+\frac{1}{K})^3-3(\rm K+\frac{1}{K})\)
⇒ 33 - 3 × 3
⇒ 27 - 9
⇒ 18
∴ The required answer is 18.
Last updated on Jul 22, 2025
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