[tex]\sqrt[3]{1-x}\stackrel{not}{=} u |()^3\\1-x= u^3 \\x=1-u^3\\\\\text{Inlocuim in ecuatia data:}\\u+\sqrt{1-u^3+8}=3\\\sqrt{9-u^3}=3-u |()^2\\9-u^3=9-6u+u^2\\u^3+u^2-6u=0\\u(u^2+u-6)=0\\\text{Distingem doua cazuri posibile:}\\i)u=0\\ii) u^2+u-6=0\\\Delta=1+24=25\Rightarrow \sqrt{\Delta}=5\\u_1=\dfrac{-1+5}{2}=2\\u_2=\dfrac{-1-5}{2}=-3\\\text{Deci }u\in \{0,2,-3\}[/tex]
[tex]\text{Pt .u=0} \Rightarrow x=1\\\text{Pt. u=2} \Rightarrow x=-7\\\text{Pt. u=-3} \Rightarrow x=28\\\text{AM obtinut solutiile :} \{1,-7,28\}\\\text{Suma modulelor este } 1+7+28=36\\\text{Raspunsul corect este a) }[/tex]
