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Daca x ∈R* si x+ 1/x = 2 , calculati x^2 + 1/x^2

Răspuns :

x+1/x =2 |²

(x+1/x)² =2²

x² + 2*x* 1/x + 1/x² =4

x² +2 +1/x² =4

x² +1/x² =4-2

x² +1/x² =2