Question

Rezolvati va rog exercitiul 2 subiectul 2

Answer 1

[tex]x+\frac{1}{x}=4 |()^2\\ \\ x^2+2\cdot x\cdot \frac{1}{x}+\frac{1}{x^2}=16\\ \\ x^2+\frac{1}{x^2}+2=16\\ \\ x^2+\frac{1}{x^2}=14\ |()^2\\ \\ x^4+2\cdot x^2\cdot \frac{1}{x^2}+\frac{1}{x^4}=196\\ \\ x^4+\frac{1}{x^4}+2=196\\ \\ \boxed{x^4+\frac{1}{x^4}=194}[/tex]