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câu b đk x>= -1/4
\(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=2\)
\(x+\sqrt{\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2}=2\)
\(\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2=2\)
\(x+\dfrac{1}{4}=\left(\sqrt{2}-\dfrac{1}{2}\right)^2\)
\(x=\left(\sqrt{2}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\)
\(x=\left(\sqrt{2}-\dfrac{1}{2}-\dfrac{1}{2}\right)\left(\sqrt{2}-\dfrac{1}{2}+\dfrac{1}{2}\right)\)
\(x=\sqrt{2}\left(\sqrt{2}-1\right)=2-\sqrt{2}\)
Giải phương trình \(\sqrt{x-2+\sqrt{2\cdot x+5}}+\sqrt{x+2+3\cdot\sqrt{2\cdot x-5}}=7\cdot\sqrt{2}\)
\(\sqrt{x-2}+2\sqrt{x-3}+\sqrt{x+6+6\sqrt{x-3}}=4\)
\(\left(\text{Đ}\text{KXĐ}:x\ge3\right)\)
\(\Leftrightarrow\sqrt{x-2}+2\sqrt{x-3}+\sqrt{\left(\sqrt{x-3}+3\right)^2}=4\)
\(\Leftrightarrow\sqrt{x-2}+2\sqrt{x-3}+\sqrt{x-3}+3=4\)
\(\Leftrightarrow\Leftrightarrow\sqrt{x-2}+3\sqrt{x-3}-1=0\)
\(\Leftrightarrow\dfrac{x-2-1}{\sqrt{x-2}+1}+3\sqrt{x-3}=0\)
\(\Leftrightarrow\dfrac{x-3}{\sqrt{x-2}+1}+\dfrac{3\left(x-3\right)}{\sqrt{x-3}}=0\)
\(\Leftrightarrow\left(\dfrac{1}{\sqrt{x-2}+1}+\dfrac{3}{\sqrt{x-3}}\right)\left(x-3\right)=0\)
Pt \(\dfrac{1}{\sqrt{x-2}+1}+\dfrac{3}{\sqrt{x-3}}\) vô no
=> x - 3 = 0
<=> x = 3 (nhận)
