Question
Download Solution PDFIf x4 + \(\frac{1}{{{x^4}}}\) = 194 and x3 + \(\frac{1}{{{x^3}}}\) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x4 + \(\frac{1}{{{x^4}}}\) = 194
Calculations:
According to question,
x4 + \(\frac{1}{{{x^4}}}\) = 194
⇒x² + 1/x² = √(194 + 2)
⇒x² + 1/x² = 14
⇒x + 1/x = √(14 + 2) = √16 = 4
now, x³ + 1/x³
= 4³ - 3(4)
= 64 - 12
= 52
Hence, The Required value is 52.
Last updated on Jul 22, 2025
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