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Daca x² + 1 supra x² = 2, calculati x + 1 supra x

Răspuns :

a²+b² = (a+b)²-2ab

x² + 1/x² = 2

=> (x + 1/x)² -2x•(1/x) = 2

=> (x + 1/x)² - 2 = 2

=> (x + 1/x)² = 4

=> x + 1/x = ±2