Question

Ex 7 dau coroana!!!!e urgent

Answer 1

$\it \sqrt{x+1}=5-x \Rightarrow \begin{cases} \it x+1\geq0 \Rightarrow x\geq-1\\ \\ \it 5-x\geq0 \Rightarrow x\leq5\end{cases} \Rightarrow -1\leq x\leq5 \Rightarrow \\ \\ \\ \Rightarrow Domeniul\ \ de\ \ existen\c{\it t}\breve a\ \ a \ ecua\c{\it t}iei\ este\ \ D=\[[-1,\ \ 5]$

$\it \sqrt{x+1}=5-x \Rightarrow (\sqrt{x+1})^2=(5-x)^2 \Rightarrow x+1=25-10x+x^2 \Rightarrow \\ \\ \Rightarrow x^2-11x+24=0 \Rightarrow x^2-3x-8x+24=0 \Rightarrow x(x-3)-8(x-3)=0 \Rightarrow \\ \\ \Rightarrow (x-3)(x-8)=0 \Rightarrow \begin{cases}\it x_1=3\in D\\ \\\it x_2=8\not\in D\end{cases}\\ \\ \\ Prin\ urmare,\ ecua\c{\it t}ia\ dat\breve a\ admite\ o \ singur\breve a \ solu\c{\it t}ie:\ \ x=3$