a/ \(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=4\)
\(\Leftrightarrow x+\sqrt{\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2}=4\)
\(\Leftrightarrow x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}=4\)
Làm nốt
b/ \(\sqrt{2x+4-6\sqrt{2x-5}}+\sqrt{2x-4+2\sqrt{2x-5}}=4\)
\(\Leftrightarrow\sqrt{\left(\sqrt{2x-5}-3\right)^2}+\sqrt{\left(\sqrt{2x-5}-1\right)^2}=4\)
Hắc Hường Mashiro Shiina Nguyễn Thanh Hằng Hiếu Cao Huy Phùng Khánh Linh Mến Vũ Hung nguyen Aki Tsuki Thiên Chỉ Hạc Trần Quốc Lộc trả lời giùm mình với
\(\text{a) }x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=4\\ \Leftrightarrow x+\sqrt{\left(x+\dfrac{1}{4}\right)+\dfrac{1}{4}+\sqrt{x+\dfrac{1}{4}}}=4\\ \Leftrightarrow x+\sqrt{\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2}=4\\ \Leftrightarrow x+\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}=4\\ \Leftrightarrow x+\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}=4\\ \Leftrightarrow\left(x+\dfrac{1}{4}\right)+\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{4}=4\\ \Leftrightarrow\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2=4\\ \Leftrightarrow\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2-4=0\\ \Leftrightarrow\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{5}{2}\right)\left(\sqrt{x+\dfrac{1}{4}}-\dfrac{3}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+\dfrac{1}{4}}+\dfrac{5}{2}=0\\\sqrt{x+\dfrac{1}{4}}-\dfrac{3}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+\dfrac{1}{4}}+\dfrac{5}{2}=0\left(Loại\right)\\\sqrt{x+\dfrac{1}{4}}=\dfrac{3}{2}\end{matrix}\right.\\ \Leftrightarrow x+\dfrac{1}{4}=\dfrac{9}{4}\\ \Leftrightarrow x=2\)
Vậy phương trình có nghiệm \(x=2\)
\(\text{b) }\sqrt{2x+4-6\sqrt{2x-5}}+\sqrt{2x-4+2\sqrt{2x-5}}=4\\ \Leftrightarrow\sqrt{\left(2x-5\right)-6\sqrt{2x-5}+9}+\sqrt{\left(2x-5\right)+2\sqrt{2x-5}+1}=4\\ \Leftrightarrow\sqrt{\left(\sqrt{2x-5}-3\right)^2}+\sqrt{\left(\sqrt{2x-5}+1\right)^2}=4\\ \Leftrightarrow\sqrt{2x-5}-3+\sqrt{2x-5}+1=4\\ \Leftrightarrow2\sqrt{2x-5}=6\\ \Leftrightarrow\sqrt{2x-5}=3\\ \Leftrightarrow2x-5=9\\ \Leftrightarrow2x=14\\ \Leftrightarrow x=7\)
Vậy phương trình có nghiệm \(x=7\)
