Q- if x square + 1/ x square = 83 then find the value of x cube - 1/ x cube
x2 + 1/x2 = 83
x2 + 1/x2 - 2 = 83 - 2
(x - 1/x)2 = 81
(x - 1/x)2 = 92
x - 1/x = 9
Now,
(x - 1/x)3 = 93
x3 - 1/x3 - 3*x*1/x (x - 1/x) = 729x3 - 1/x3 - 3*x*1/x (x - 1/x) = 729
now substituting the value of x - 1/x
x3 - 1/x3 - 3*9 = 729
x3 - 1/x3 - 27 = 729
x3 - 1/x3 = 729 + 27
x3 - 1/x3 = 756