If x - 1/2x = 4, then the value of 8x^3 -1/(x^3) will be :

We know that,

If x - y  = n

then, $x^3 - y^3$ = n³ + 3 × n × xy

If $x - \frac{1}{2x} = 4$,

x³ - \(\frac{1}{8x^3}\) = 4³ + 3 × 4 × \(\frac{1}{2}\) = 70

Multiply the above equation by 8 to get the desired form of result =

then the value of $8x^3 -\frac{1}{x^3}$ will be = 70 × 8 = 560