Question

Care sunt solutiile ecuatiei $|-m^{2} + m|=6$

Answer 1

Răspuns:

Explicație pas cu pas:

$\texttt{Avem doua cazuri de analizat.}\\ i)-m^2+m=6\\-m^2+m-6=0\\\Delta=1-4\cdot 6=-23<0\Rightarrow \texttt{ecuatia nu admite solutiile reale.}\\ii)-m^2+m=-6\\-m^2+m+6=0\\\Delta=1+4\cdot 6=1+24=25\Rightarrow \sqrt{\Delta}=5\\m_1=\dfrac{-1+5}{-2}=-2\\m_2=\dfrac{-1-5}{-2}=3\\S=\{-2,3\}$