[tex]z + \frac{25}{z} = 6[/tex]
[tex]z + \frac{25}{z} - 6 = 0 | \times z[/tex]
[tex] {z}^{2} + 25 - 6z = 0[/tex]
[tex] {z}^{2} - 6z + 25 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = - 6[/tex]
[tex]c = 25[/tex]
[tex]delta = {b}^{2} - 4ac[/tex]
[tex]delta = {( - 6)}^{2} - 4 \times 1 \times 25[/tex]
[tex]delta = 36 - 100[/tex]
[tex]delta = - 64 < 0[/tex]
[tex] = >ecuatia \: nu \: are \: radacini \: reale[/tex]
[tex] = > ecuatia \: are \: radacini \: compexe[/tex]
[tex] = > x1.2 = \frac{ - b + - i \sqrt{ delta} }{2a} [/tex]
[tex]x1 = \frac{ - b + i\sqrt{ delta} }{2a} [/tex]
[tex]x1 = \frac{ - ( - 6) + i \sqrt{ - 64} }{2 \times 1} [/tex]
[tex]x1 = \frac{6 + \sqrt{ - 64 \times {i}^{2} } }{2} [/tex]
[tex]x1 = \frac{6 + \sqrt{ - 64 \times ( - 1)} }{2} [/tex]
[tex]x1 = \frac{6 + \sqrt{64} }{2} [/tex]
[tex]x1 = \frac{6 + 8}{2} [/tex]
[tex]x1 = \frac{14}{2} [/tex]
[tex]x1 = 7[/tex]
[tex]x2 = \frac{ - b - i \sqrt{delta} }{2a} [/tex]
[tex]x2 = \frac{ - ( - 6) - i \sqrt{64} }{2 \times 1} [/tex]
[tex]x2 = \frac{6 - i \sqrt{64} }{2} [/tex]
[tex]x2 = \frac{6 - \sqrt{ ( - 64) \times {i}^{2} } }{2} [/tex]
[tex]x2 = \frac{6 - \sqrt{( - 64) \times ( - 1)} }{2} [/tex]
[tex]x2 = \frac{6 - \sqrt{64} }{2} [/tex]
[tex]x2 = \frac{6 - 8}{2} [/tex]
[tex]x2 = \frac{ - 2}{2} [/tex]
[tex]x2 = - \frac{2}{2} [/tex]
[tex]x2 = - 1[/tex]
