p – 1/p = √7, అయితే p3 – 1/p3 విలువ ఎంత?

  1. 12√7
  2. 4√5
  3. 8√7
  4. 10√7

Answer (Detailed Solution Below)

Option 4 : 10√7
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Detailed Solution

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ఇచ్చినది:

p – 1/p = √7

ఫార్ములా:

P3 – 1/p3 = (p – 1/p)3 + 3(p – 1/p)

లెక్కింపు:

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

చిన్న ఉపాయం

x - 1/x = a, అప్పుడు x3 - 1/x3 = a3 + 3a

ఇక్కడ, a = √5

ఇక్కడ,

p3 – 1/p3 = (√7)3 + 3 × √7 = 7√7 + 3√7 = 10√7.

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