Question

Giải phương trình; \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)

Answer 1

\(\sqrt{2}.\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{2}.\sqrt{x-2-\sqrt{2x-5}=4}\)

=>\(\sqrt{2x-5+2.3\sqrt{2x-5}+9}+\sqrt{2x-5+2\sqrt{2x-5}+1}=4\)

=>\(\sqrt{\left(\sqrt{2x-5}+3\right)^2}+\sqrt{\left(\sqrt{2x-5}-1\right)^2}=4\)

=>\(|\sqrt{2x-5}+3|+|\sqrt{2x-5}-1|=4\)

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Answer 2

tích mình đi

ai tích mình

mình ko tích lại đâu

thanks

Answer 3

tích mình đi

ai tích mình

mình ko tích lại đâu

thanks

Answer 4

Haha con chố !

Answer 5

Điều kiện \(x\ge\frac{5}{2}\)

\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-2\sqrt{2x-5}}=2\sqrt{2}\)

\(\Leftrightarrow\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

\(\Leftrightarrow\sqrt{2x-5+6\sqrt{2x-5}+9}+\sqrt{2x-5-2\sqrt{2x-5}+1}=4\)

\(\Leftrightarrow\sqrt{\left(\sqrt{2x-5}+3\right)^2}+\sqrt{\left(1-\sqrt{2x-5}\right)^2}=4\)

\(\Leftrightarrow\left|\sqrt{2x-5}+3\right|+\left|1-\sqrt{2x-5}\right|=4\)

\(\Leftrightarrow\sqrt{2x-5}+3+\left|1-\sqrt{2x-5}\right|=4\)

\(\Leftrightarrow\left|1-\sqrt{2x-5}\right|=1-\sqrt{2x-5}\)

\(\Leftrightarrow1-\sqrt{2x-5}\ge0\)

\(\Leftrightarrow\sqrt{2x-5}\le1\Leftrightarrow\frac{5}{2}\le x\le3\)