Question

rezolvati:(x-1)²+4=x​

Answer 1

 

$\displaystyle\bf\\(x-1)^2+4=x\\\\(x-1)^2+4-x=0\\\\x^2-2x+1+4-x=0\\\\x^2-3x+5=0\\\\x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{3\pm\sqrt{9-20}}{2}=\frac{3\pm\sqrt{-11}}{2}\\\\\Delta~este~negativ.\\Rezulta~ca~ecuatia~nu~are~solutii~in~R,\\dar~are~solutii~in~.C\\\\x_1=\frac{3-\sqrt{-11}}{2}=\frac{3-i\sqrt{11}}{2}=\boxed{\bf\frac{3}{2}-\frac{\sqrt{11}}{2}i}\\\\\\x_2=\frac{3+\sqrt{-11}}{2}=\frac{3+i\sqrt{11}}{2}=\boxed{\bf\frac{3}{2}+\frac{\sqrt{11}}{2}i}$