Question

z+25/z=6.Rezolvati ec.
Repede va rog...e cu nr.complexe.

Answer 1

$z + \frac{25}{z} = 6$

$z + \frac{25}{z} - 6 = 0 | \times z$

${z}^{2} + 25 - 6z = 0$

${z}^{2} - 6z + 25 = 0$

$a = 1$

$b = - 6$

$c = 25$

$delta = {b}^{2} - 4ac$

$delta = {( - 6)}^{2} - 4 \times 1 \times 25$

$delta = 36 - 100$

$delta = - 64 < 0$

$= >ecuatia \: nu \: are \: radacini \: reale$

$= > ecuatia \: are \: radacini \: compexe$

$= > x1.2 = \frac{ - b + - i \sqrt{ delta} }{2a}$

$x1 = \frac{ - b + i\sqrt{ delta} }{2a}$

$x1 = \frac{ - ( - 6) + i \sqrt{ - 64} }{2 \times 1}$

$x1 = \frac{6 + \sqrt{ - 64 \times {i}^{2} } }{2}$

$x1 = \frac{6 + \sqrt{ - 64 \times ( - 1)} }{2}$

$x1 = \frac{6 + \sqrt{64} }{2}$

$x1 = \frac{6 + 8}{2}$

$x1 = \frac{14}{2}$
$x1 = 7$

$x2 = \frac{ - b - i \sqrt{delta} }{2a}$

$x2 = \frac{ - ( - 6) - i \sqrt{64} }{2 \times 1}$

$x2 = \frac{6 - i \sqrt{64} }{2}$

$x2 = \frac{6 - \sqrt{ ( - 64) \times {i}^{2} } }{2}$

$x2 = \frac{6 - \sqrt{( - 64) \times ( - 1)} }{2}$

$x2 = \frac{6 - \sqrt{64} }{2}$

$x2 = \frac{6 - 8}{2}$

$x2 = \frac{ - 2}{2}$

$x2 = - \frac{2}{2}$

$x2 = - 1$