Răspuns:
Explicație pas cu pas:
x + 1/x = 2
ridici la patrat
(x + 1/x)^2 = 2^2
x^2 + 2*x*1/x + 1/x^2 = 4
x^2 + 2 + 1/x^2 = 4
x^2 + 1/x^2 = 4 - 2
x^2 + 1/x^2 = 2
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(x + 1/x)^3 = 2^3
(x + 1/x)(x + 1/x)^2 = 8
(x + 1/x)(x^2 + 2 + 1/x^2) = 8
x^3 + 2x + 1/x + x + 2/x + 1/x^3 = 8
x^3 + 1/x^3 + 3x + 3/x = 8
x^3 + 1/x^3 + 3*(x + 1/x) = 8
x^3 + 1/x^3 + 3*2 = 8
x^3 + 1/x^3 = 8 - 6 = 2
