Question

m^3+3m^2-9m>=0,......... m=?

Answer 1

[tex]m^3+3m^2-9m\geq 0\\ m(m^2+3m-9)\geq0\\ \text{Sa aflam radacinile ecuatiei de gradul 2.}\\ m^2+3m-9=0\\ \Delta=9+36=45\Rightarrow \sqrt{\Delta}=3\sqrt5\\ m_1=\dfrac{-3+3\sqrt5}{2},m_2=\dfrac{-3-3\sqrt5}{2}\\ \text{Facem un tabel de semn:} [/tex]
[tex] ~~~~~~~~~~~~~~~~~~ | ~~~~\dfrac{-3-3\sqrt5}{2}~~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~\dfrac{-3+3\sqrt5}{2}\\ ~~~~~m~~~~~~~~~~|-~~~~~-~~~~~~~~~-~~~~~~~~0~~~~~+~~~~~~~+~~~~~~~+\\ m^2+3m-9|++~~~~0~~~~-~~~~~~~~~~~~-~~~~~~~-~~~~~~~~~~~~~0~~~+~~~+\\ ~~~~~~~~~~~~~~~~~~|-~~~~~~0~~~~~~~~~+~~~~~~~~~0~~~~~~~~~~~-~~~~~~~~~0~~~~~~~~~~~~+\\ S:m\in \left[\dfrac{-3-3\sqrt5}{2},0\right]\cup \left[\dfrac{-3+3\sqrt5}{2},\infty\left)[/tex]