Giải:
\(\sqrt{\dfrac{x+1}{2}}=\dfrac{\sqrt{5}}{2}\)
\(\Leftrightarrow\dfrac{\sqrt{x+1}}{\sqrt{2}}=\dfrac{\sqrt{5}}{2}\)
\(\Leftrightarrow2.\sqrt{x+1}=\sqrt{5}.\sqrt{2}\)
\(\Leftrightarrow2.\sqrt{x+1}=\sqrt{10}\)
\(\Leftrightarrow\sqrt{x+1}=\dfrac{\sqrt{10}}{\sqrt{4}}\)
\(\Leftrightarrow\sqrt{x+1}=\sqrt{\dfrac{10}{4}}\)
\(\Leftrightarrow x+1=\dfrac{10}{4}\)
\(\Leftrightarrow x=\dfrac{10}{4}-1=\dfrac{3}{2}\)
Vậy \(x=\dfrac{3}{2}\).
Chúc bạn học tốt!
\(\sqrt{\dfrac{x+1}{2}}=\dfrac{\sqrt{5}}{2}\)
\(=\dfrac{\sqrt{x+1}}{\sqrt{2}}=\dfrac{\sqrt{5}}{2}\)
\(=\sqrt{x+1}.2=\sqrt{5}.\sqrt{2}\)
\(=\sqrt{x+1}.2=\sqrt{10}\)
\(=\sqrt{x+1}=\dfrac{\sqrt{10}}{\sqrt{4}}\left(\sqrt{4}=2\right)\)
\(=\sqrt{x+1}=\sqrt{\dfrac{10}{4}}\)
\(\sqrt{x+1}=\sqrt{\dfrac{5}{2}}\)
\(\Rightarrow x+1=\dfrac{5}{2}\Rightarrow x=\dfrac{5}{2}-1=1\dfrac{1}{2}=\dfrac{3}{2}\)
Vậy \(x=\dfrac{3}{2}\)