1rút gọn\(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}\) \(\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)}^2\)2giải pt\(\sqrt{9x+18}-5\sqrt{x+2}+\frac{4}{5}\sqrt{25x+50}=6\) 3cho btP=\(\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{\sqrt{x+1}}+\frac{2}{x-1}\right)\) tìm đk b, rút...
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1rút gọn
\(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}\) \(\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)}^2\)
2giải pt
\(\sqrt{9x+18}-5\sqrt{x+2}+\frac{4}{5}\sqrt{25x+50}=6\)
3cho bt
P=\(\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{\sqrt{x+1}}+\frac{2}{x-1}\right)\)
tìm đk
b, rút gọn
B1:
\(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}\)
\(=\left|\sqrt{2}-\sqrt{3}\right|+3\sqrt{2}\)
\(=\sqrt{3}-\sqrt{2}+3\sqrt{2}\)
\(=\sqrt{3}+2\sqrt{2}\)
\(\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)^2}\)
\(=\sqrt{4-4\sqrt{3}+3}+\left|1+\sqrt{3}\right|\)
\(=\sqrt{\left(2-\sqrt{3}\right)^2}+1+\sqrt{3}\)
\(=2-\sqrt{3}+1+\sqrt{3}\)
\(=3\)
B2:
đk: \(x\ge-2\)
Ta có: \(\sqrt{9x+18}-5\sqrt{x+2}+\frac{4}{5}\sqrt{25x+50}=6\)
\(\Leftrightarrow3\sqrt{x+2}-5\sqrt{x+2}+4\sqrt{x+2}=6\)
\(\Leftrightarrow2\sqrt{x+2}=6\)
\(\Leftrightarrow\sqrt{x+2}=3\)
\(\Leftrightarrow x+2=9\)
\(\Rightarrow x=7\)
Vậy x = 7