Do obliczenia: [tex]a+\frac{1}{a}[/tex]
Wiemy, że: [tex]a^2+\frac{1}{a^2}=5[/tex]
Podnieśmy do kwadratu wyrażenie [tex]a+\frac{1}{a}[/tex]
[tex](a+\frac{1}{a})^2=a^2+2*a*\frac{1}{a}+(\frac{1}{a})^2=a^2+2+\frac{1}{a^2}=a^2+\frac{1}{a^2}+5=5+2=7[/tex]
Zatem
[tex](a+\frac{1}{a})^2=7/\sqrt{ }\\a+\frac{1}{a}=\sqrt{7}[/tex]