Question

(a la patrat +1)x la patrat-2x+1=0

Answer 1

 

$\displaystyle\bf\\Se~da~ecuatia:\\\\(a^2+1)x^2-2x+1=0\\\\Se~cere:\\\\Sa~demonstram~ca~ecuatia~ nu~admite~radacini~reale,~\forall~a \in R^{\bigstar}\\\\Rezolvare:\\\\Calculam~discriminantul~\Delta.\\\\\Delta=b^2-4ac\\\\\Delta=(-2)^2-4(a^2+1)\cdot 1\\\\\Delta=4-4-4a^2\\Delta=-4a^2\\\\a^2>0~~\forall~a \in R^{\bigstar}\\\implies -a^2 <0\\\implies -4a^2 <0\\\implies~\boxed{\bf\Delta<0}\\\\\implies~\boxed{\bf~Ecuatia~ nu~admite~radacini~reale.}$