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Daca x+1/x=3,calculati a)X²+1/X² b)x³+1/x³.

Răspuns :

a)  (x+1/x)^2=3^2
x^2+2+1/x^2=9
x^2+1/x^2=7
b)  (x+1/x)^3=x^3+1/x^3+3(x+1/x)
x^3+1/x^3=(x+1/x)^3-3(x+1/x)=3^3-3*3=27-9=18