Stim [tex]a^{2} + \frac{1}{a^{2}} = 7[/tex] si [tex]s = a + \frac{1}{a}[/tex]
Atunci,
[tex]s^{2} = (a+\frac{1}{a})^{2}[/tex]
[tex]s^{2} = a^{2} + (\frac{1}{a})^{2} + 2a\frac{1}{a}[/tex]
[tex]s^{2} = a^{2} + \frac{1}{a^{2}} + 2[/tex]
[tex]s^{2} - 2 = a^{2} + \frac{1}{a^{2}}[/tex]
[tex]s^{2} - 2 = 7[/tex]
[tex]s^{2} = 9[/tex]
[tex]s_1 = -3[/tex] si [tex]s_2 = + 3[/tex]
Deci, S = { -3; 3 }
Mult noroc
Mexic
