#SSC CGL

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Question : If $p-\frac{1}{p}=6$, then what is the value of $p^4+\frac{1}{p^4}$?
Option 1: 1562
Option 2: 1432
Option 3: 1442
Option 4: 1444

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Team Careers360 24th Jan, 2024

Answer (1)

Team Careers360 25th Jan, 2024

Correct Answer: 1442

Solution : $\mathrm{p}-\frac{1}{\mathrm{p}}=6$
Squaring both sides, we get,
$⇒p^2+\frac{1}{p^2}-2(p)(\frac{1}{p})=36$
$⇒p^2+\frac{1}{p^2}-2=36$
$⇒p^2+\frac{1}{p^2}=38$
Squaring both sides again, we get,
$⇒p^4+\frac{1}{p^4}+2(p^2)(\frac{1}{p^2})=1444$
$⇒p^4+\frac{1}{p^4}+2=1444$
$\therefore p^4+\frac{1}{p^4}=1442$
Hence, the correct answer is 1442.

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