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\(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)
\(2x+5\sqrt{x}-3=\left(\sqrt{x}+3\right)\left(2\sqrt{x}-1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x-6\sqrt{x-3}+6\text{=}x-3-6\sqrt{x-3}+9\)
\(\text{=}\left(\sqrt{x-3}\right)^2-2.3.\sqrt{x-3}+\left(3\right)^2\)
\(\text{=}\left(\sqrt{x-3}-3\right)^2\)
A = \(x-6\)\(\sqrt{x-3}\) + 6 (đkxd \(x>3\))
A = (\(x\) - 3) - 2.3.\(\sqrt{x-3}\) + 9
A = (\(\sqrt{x-3}\))2 - 2.3.\(\sqrt{x-3}\) + 32
A = (\(\sqrt{x-3}\)- 3)2
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\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)
\(=2+\sqrt{3}+\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right)\left(\sqrt{2}+1\right)\)
\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x+7\sqrt{x}+10=\left(\sqrt{x}+2\right)\left(\sqrt{x}+5\right)\)
\(8-\frac{x\sqrt{x}}{3}\)
\(=8-\frac{\sqrt{x^3}}{3}\)
\(=8-\frac{\left(\sqrt{x}\right)^3}{3}\)
\(=8-\frac{\left(\sqrt{x}\right)^3}{\left(\sqrt[3]{3}\right)^3}\)
\(=2^3-\left(\frac{\sqrt{x}}{\sqrt[3]{3}}\right)^3\)
\(=\left(2-\frac{\sqrt{x}}{\sqrt[3]{3}}\right)\left(4+\frac{2\sqrt{x}}{\sqrt[3]{3}}+\frac{x}{\left(\sqrt[3]{3}\right)^2}\right)\)