Question
Download Solution PDFIf p – 1/p = √7, then find the value of p3 – 1/p3.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
p – 1/p = √7
Formula:
P3 – 1/p3 = (p – 1/p)3 + 3(p – 1/p)
Calculation:
P3 – 1/p3 = (p – 1/p)3 + 3 (p – 1/p)
⇒ p3 – 1/p3 = (√7)3 + 3√7
⇒ p3 – 1/p3 = 7√7 + 3√7
⇒ p3 – 1/p3 = 10√7
Shortcut Trick x - 1/x = a, then x3 - 1/x3 = a3 + 3a
Here, a = √7 ( put the value in required eqn )
⇒p3 – 1/p3 = (√7)3 + 3 × √7 = 7√7 + 3√7
⇒p3 – 1/p3 = 10√7.
Hence; option 4) is correct.
Last updated on Jul 4, 2025
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