Question

(p - 1/p) = 5 , prove that p ^ 3 - 1/(p ^ 3) = 140​

Answer 1

Use identity:

• a³ - b³ = (a - b)(a² + ab + b²),

Modify it as follows:

• a³ - b³ =
• (a - b)(a² + ab + b²) =
• (a - b)(a² - 2ab + b² + 3ab) =
• (a - b)[(a - b)² + 3ab]

Substitute a = p, b = 1/p and evaluate:

• p³ - 1/p³ =
• (p - 1/p)[(p - 1/p)² + 3p(1/p)] =
• 5(5² + 3) =
• 5(25 + 3) =
• 5(28) =
• 140

Proved