Question

rexolvati ecuatia bibatrata xla 4-7x2+12=0​

Answer 1

   

$\displaystyle\bf\\x^4-7x^2+12=0\\\\Substitutie:~~~\boxed{\bf x^2=y}\\\\y^2-7y+12=0\\\\y_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{7\pm\sqrt{49-4\times12}}{2}=\frac{7\pm\sqrt{49-48}}{2}=\frac{7\pm1}{2}\\\\ y_1=\frac{7+1}{2}=\frac{8}{2}=4\\\\ y_2=\frac{7-1}{2}=\frac{6}{2}=3\\\\Ne~intoarcem~la~substitutie:\\\\x^2=y\\\\x_{12}=\pm\sqrt{y_1}=\pm\sqrt{4} \\\\x_1=2\\\\x_2=-2\\\\x_{34}=\pm\sqrt{y_2}=\pm\sqrt{3}\\\\ x_3=\sqrt{3}\\\\ x_4=-\sqrt{3}$