Question

Anutoŕrrrrrrrrrrrrrrrrrrrrrrrrrrrrr.......

Answer 1

[tex]E=\sqrt{x^3+3x^2+2x}\\ \text{Radicalul(de ordin par)este de.finit daca ceaa ce se afla sub el este}\geq 0\\ \text{Deci avem ca:}\\ x^3+3x^2+2x\geq 0\\ x(x^2+3x+2)\geq 0\\ x(x^2+2x+x+2)\geq 0\\ x(x+1)(x+2)\geq 0\\ \text{Facem tabel de semn.} [/tex]
[tex]x~~~~~~|-\infty ~- ~~ -3~-~~-2~-~~~~0~~~~~~~+~~~~~~~~~~~~~~~~~~\infty \\ ^{------------------------------------------------}\\ x+2~|~~~~~~~~~~-~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~+~~~~~~~ \\ ^{-----------------------------------------------}\\ x+3~| ~~~~~-~~~~~~~~0~~~~~~~~~~~~~~~~~~~+\\ ^{-----------------------------------------------}\\ E(x)~| ~~~~~~-~~~~~~~0~~~+~~~0~~~-~~~0~~~~~~~~~~~~~+\\ ^{-----------------------------------------------}\\ Deci\ x\in[-3,-2]\cup [0,\infty] [/tex]