Question

x^3-1/x^3 if x^2+1/x^2=18​

Answer 1

=> x^2 + (1/x^2) = 18

=> x^2 + (1/x^2) = 2 + 16

=> x^2 + 1/x^2 - 2 = 16

=> (x - 1/x)^2 = 16

=> x - (1/x) = 4

Find x^3 - 1/x^3 :

=> (x - 1/x)^3 = x^3 - 1/x^3 - 3(x - 1/x)

=> (4)^3 = x^3 - 1/x^3 - 3(4)

=> 64 = x^3 - 1/x^3 - 12

=> x^3 - 1/x^3 = 76

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