Question
Download Solution PDFIf \(x+\frac{1}{x}=7\), find the value of \(x^3+\frac{1}{x^3}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
If \(x+\frac{1}{x}=7\), find the value of \(x^3+\frac{1}{x^3}\).
Formula used:
\((x + \frac{1}{x})^3 = x^3 + \frac{1}{x^3} + 3(x + \frac{1}{x})\)
Calculation:
\(x+\frac{1}{x}=7\)
⇒ \( (x+\frac{1}{x})^3 = 7^3 \)
⇒ \( x^3 + \frac{1}{x^3} + 3(x+\frac{1}{x}) = 343 \)
⇒ \( x^3 + \frac{1}{x^3} + 3 \times 7 = 343 \)
⇒ \( x^3 + \frac{1}{x^3} + 21 = 343 \)
⇒ \( x^3 + \frac{1}{x^3} = 343 - 21 \)
⇒ \( x^3 + \frac{1}{x^3} = 322 \)
∴ The correct answer is option (4).
Last updated on Jun 3, 2025
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