[tex] {x}^{2} - 2x + {a}^{2} + 1 = 0[/tex]
[tex]m= 1[/tex]
[tex]n = - 2[/tex]
[tex]p= {a}^{2} + 1[/tex]
[tex]s = x_{1} + x_{2} = - \frac{n}{m} = - \frac{ - 2}{1} = 2[/tex]
[tex]p = x_{1} x_{2} = \frac{p}{m} = \frac{ {a}^{2} + 1 }{1} = {a}^{2} + 1[/tex]
[tex]2x_{1} + 2x_{2} + x_{1}x_{2} = 9[/tex]
[tex]2(x_{1} + x_{2}) + x_{1}x_{2} = 9[/tex]
[tex]2s + p = 9[/tex]
[tex]2 \times 2 + {a}^{2} + 1 = 9[/tex]
[tex]4 + {a}^{2} + 1 = 9[/tex]
[tex] {a}^{2} = 9 - 4 - 1[/tex]
[tex] {a}^{2} = 4[/tex]
[tex]a = \pm \sqrt{4} [/tex]
[tex]a = \pm2[/tex]
