Question

Determinati toate solutiile complexe ale ecuatiei.
x la puterea a 4-5x la a 2 -36=0

Answer 1

$\displaystyle\\ x^4-5x^2-36=0\\\\ \text{Facem substitutia: }~~y=x^2\\\\ y^2-5y-36=0\\\\ y_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{5\pm \sqrt{25+144}}{2}=\\\\ =\frac{5\pm \sqrt{169}}{2}=\frac{5\pm 13}{2}\\\\ y_1 = \frac{5+ 13}{2}=\frac{18}{2}=9\\\\ y_2 = \frac{5-13}{2}=\frac{-8}{2}=-4\\\\ \text{Ne intoarcem la substitutie.}\\\\ x^2 = 9\\ x = \pm\sqrt{9} \\ x_1 = 3\\ x_2=-3\\\\ x^2=-4\\ x=\pm\sqrt{-4}\\ x_3 = 2i\\ x_4 = -2i$