Question

Află valorile necunoscutei x pentru care are sensul epresiei : $\sqrt{4x-8}+ \sqrt{10-2x}$

Answer 1

  
[tex]\displaystyle \\ \texttt{Sub radical trebuie sa fie } \geq 0\\ \\ \texttt{Din primul radical: } \\ 4x-8 \geq 0 \\ 4x \geq 8 \\ \\ x \geq \frac{8}{4} \\ \\ \boxed{x \geq 2} \\ \\ \\ \texttt{Din al doilea radical: } \\ 10 - 2x \geq 0 \\ - 2x \geq -10 ~~~~~| \cdot (-1)\\ 2x \leq 10 \\ \\ x \leq \frac{10}{2} \\ \\ \boxed{x \leq 5 } \\ \\ \texttt{Din } ~~\boxed{x \geq 2} ~~\texttt{ si }~~ \boxed{x \leq 5 } ~~\Longrightarrow ~~ \boxed{ \boxed{x \in [2, 5]}}[/tex]


 

Answer 2

√4x-8+√10-2x=
(√4x-8)²+(√10-2x)=
4x-8+10-2x=0
2x=-2
x=-2/2
x=-1