Question

if x$if x-1/x=5, x^{3}-1/x^{3}=?$

Answer 1

$x-\frac{1}{x}=5\\\\x^3-\frac{1}{x^3}=?\\\\(x-\frac{1}{x})^3=x^3-\frac{1}{x^3}-3\ x^2\ \frac{1}{x}+3\ x\ \frac{1}{x^2}\\\\=x^3-\frac{1}{x^3}-3\ x+3\frac{1}{x}\\\\=x^3-\frac{1}{x^3}-3\ (x-\frac{1}{x})\\\\x^3-\frac{1}{x^3}=5^3+3*5\\\\=140$