Question

cum rezolv : -x^3-3x^2-3x-7=0

Answer 1

Stim ca in general
$(x+1)^{3}=x^{3}+3x^{2}+3x+1$
Atunci ecuatia noastra(sa o notam cu E) devine
$E=-(x^{3}+3x^{2}+3x+7)=-(x^{3}+3x^{2}+3x+1+6)=-(x+1)^{3}-6=0\Rightarrow (x+1)^{3}=-6\Rightarrow x+1=(-6)^{\frac{1}{3}}\Rightarrow x=-1-6^{\frac{1}{3}}$
Toate cele 3 solutii sunt identice cu cea de mai sus.