Question
Download Solution PDFIf p – \(\frac{1}{p}\) = 6, then what is the value of p4 + \(\frac{1}{{{p^4}}}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The expression \(p-\frac{1}{p}=6\)
Formula Used:
a2 + b2 = (a - b)2+ 2ab
Calculation:
p4 + \(\frac{1}{p^4}\)
⇒ (p2+\(\frac{1}{p^2}\))2 - 2 × p2 × \(\frac{1}{p^2}\)
⇒ {(p-\(\frac{1}{p}\))2+ (2 × p × \(\frac{1}{p}\))}2 - 2
⇒ {(6)2 + 2}2 - 2
⇒ (36 + 2)2 - 2
⇒ (38)2 - 2
⇒ 1444 - 2
⇒ 1442
Hence the value of the expression p4 +\(\frac{1}{p^4}\) is 1442.
Last updated on Jun 13, 2025
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