Question

Ecuații bipătrate :
a) z la 2-8=-25 pe z la 2
b) z la 2 +9 pe z la 2 = 2
Vă rog frumos cine se pricepe să-mi şi explice cum a rezolvat. Mulțumesc frumos!

Answer 1

[tex]a)z^2-8=-\frac{25}{z^2}| \cdot z^2\\ z^4-8z^2=-25\\ (z^2)^2-8z^2+25=0\\ \Delta=64-4\cdot 25=-36\Rightarrow \sqrt{\Delta}=6i\\ z_1=\frac{8-6i}{2}=\boxed{4-3i}\\ z_2=\frac{8+6i}{2}=\boxed{4+3i}\\ S:z\in \{4\pm 3i\}[/tex]
[tex]b)z^2+\frac{9}{z^2}=2| \cdot z^2\\ (z^2)^2+9=2z^2\\ (z^2)^2-2z^2+9=0\\ \Delta=4-4\cdot 9=-32\Rightarrow \sqrt{\Delta}=4i\sqrt2 \\ z_1=\frac{2+4i\sqrt2}{2}=1+2i\sqrt2\\ z_2=\frac{2-4i\sqrt2}{2}=1-2i\sqrt2\\ S:z\in \{1\pm 2i\sqrt2\}[/tex]