Răspuns:
10.
Explicație pas cu pas:
[tex]x+\frac{1}{x}=\sqrt{5},~|^2,~=>~(x+\frac{1}{x})^2=(\sqrt{5})^2,~=>~x^2+2*x*\frac{1}{x}+(\frac{1}{x}) ^2=5,~=>~x^2+2+ \frac{1}{x^2}=5,~=>~x^2+\frac{1}{x^2}=5-2,~=>~x^2+\frac{1}{x^2}=3.~~(1)\\ x^2+\frac{1}{x^2}=3,~|^2,~=>~(x^2+\frac{1}{x^2})^2=3^2,~=>~x^4+2+\frac{1}{x^4}=9,~=>~x^4+\frac{1}{x^4}=7.~~(2).\\Atunci~E(x)=x^2+\frac{1}{x^2}+x^4+\frac{1}{x^4}=3+7=10[/tex]
