Question

If p-1/p =8, find the value of p^3 - 1/p ^3

Answer 1

Cubing both side
P^3 -1\p^3 - 3(8) = 512 [(a-b)^3 = a^3 - b^3 - 3ab(a-b) ... and value of a-b is given]
P^3 - 1/p^3 = 512+24= 536

Answer 2

Answer:

★$\huge\boxed{Answer}$★

${p} - \frac{1}{ {p}} = 8$

${p}^{3} - \frac{1}{ {p}^{3} } = ?$

$( {p - \frac{1}{p} } ) ^{3} = \\ {p}^{3} - \frac{1}{p ^3} - 3 \times p \times \frac{1}{p} (p - \frac{1}{p} )$

$( 8) ^{3} = {p}^{3} - \frac{1}{p ^3 } - 3 \times (8)$

$512 = {p}^{3} - \frac{1}{ {p}^{3} } - 24$

$512 + 24 = {p}^{3} - \frac{1}{ {p}^{3} }$

$536 ={p}^{3} - \frac{1}{ {p}^{3} }$

${p}^{3} - \frac{1}{ {p}^{3} } = 536$

536 is your answer