Question

if x cube + 1 upon x cube is equals to M and X square + 1 upon x square is equals to 47 find the value of m

Answer 1

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) = +/- 729

Now, substituting the value of x - 1/x, we get,

x3 - 1/x3 - 3*9 = 729  and x3 - 1/x3 + 3*9 = -729

x3 - 1/x3 - 27 = 729  and x3 - 1/x3 + 27 = -729

x3 - 1/x3 = 756 and x3 - 1/x3 = -756