Question

Cum rezolv: -m^3 +3m +2=0?

Answer 1

   
[tex]\displaystyle\\ -m^3 +3m +2=0\\ \text{Cautam o solutie printre divizorii intregi ai termenului liber.}\\ D_2=\{-2;~-1;~1;~2\}\\ \text{Observam ca 2 este o solutie a ecuatiei.}\\ {\bf -2^3 + 3\cdot 2 + 2 = -8 + 6 + 2 = 0}\\\\ \text{Organzam convenabil termenii ecuatiei, astfel incat sa }\\ \text{descompunem expresia de gradul 3 intr-un }\\ \text{produs dintre (m - 2) si o expresie de gradul 2.} [/tex]

[tex]\displaystyle \bf\\ -m^3 +3m +2=0\\ -m^3 + 2m^2 - 2m^2+4m - m +2=0~~~~~\text{Dam factor comun.}\\ -m^2(m - 2) - 2m(m-2) - (m -2)=0~\text{Dam factor comunpe m-2).}\\ (m-2)(-m^2-2m-1)=0\\\\ m-2=0\\ \boxed{\bf m_1 =2}\\\\ -m^2-2m-1 = 0~~~\Big|~\times(-1)\\ m^2+2m+1 = 0\\\\ m_{23}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}= \frac{-2\pm \sqrt{4-4}}{2} =\frac{-2\pm \sqrt{0}}{2}=\frac{-2}{2}=-1\\\\ \boxed{\bf m_2 = m_3 = -1}~~~~~\text{\bf (radacina dubla)}[/tex]