if xsquare+1/xsquare=83, then find xcube-1/xcube?

Asked by kartikeya vimal | 17th Jun, 2013, 06:10: PM

Expert Answer:

x2 + 1/x= 83

x+ 1/x2 - 2 = 83 - 2

(x - 1/x)2 = 81

(x - 1/x)= 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

Answered by  | 17th Jun, 2013, 10:01: PM

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