If $ p^4 = 4354 -\frac{1}{p^4}$ then the value of $p^3 - \frac{1}{p^3}$ can  be :

536

If x⁴ + \(\frac{1}{x^4}\) = a

then x² + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\) = b

and x - \(\frac{1}{x}\) = \(\sqrt {b - 2}\)

If $ p^4 = 4354 -\frac{1}{p^4}$

then the value of $p^3 - \frac{1}{p^3}$ = ?

If $ p^4 = 4354 -\frac{1}{p^4}$

$ p^4 + \frac{1}{p^4}= 4354 $

p² + \(\frac{1}{p^2}\) = \(\sqrt {4356 + 2}\) = 66

and p - \(\frac{1}{p}\) = \(\sqrt {66 - 2}\) = 8

If x - \(\frac{1}{x}\)  = n

then, $x^3 -\frac{1}{x^3}$ = n³ + 3 × n

$p^3 - \frac{1}{p^3}$ = 8³ + 3 × 8

$p^3 - \frac{1}{p^3}$ = 512 + 24= 536