Question

If x+1/x=10 find the value of x^3-1/x^3

Answer 1

a^3-b^3=(a-b)^3+3ab(a+b)
x-1/x= √(x+1/x) ^2-4=√10^2-4=√96=4√6

hence x3-1/x^3 = (x-1/x)^3+3*x*1/x(x-1/x)= 64*6√6+3*4√6