\(\sqrt{\left(5+2\sqrt{6}\right)}+\sqrt{8-2\sqrt{15}}\)

\(=\sqrt{\left(2+2.\sqrt{2}.\sqrt{3}+3\right)}+\sqrt{3-2\sqrt{3}.\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}\)

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

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

Ta có: \(\sqrt{5}< \sqrt{16}\left(=4\right)\)

\(\Rightarrow\sqrt{5}-4< 0\)

\(mà2\sqrt{3}>0\)

\(\Rightarrow2\sqrt{3}>\sqrt{5}-4\)

Ta có: \(\sqrt{5}< \sqrt{12}\)và \(-4< 0\)

\(\Rightarrow\sqrt{5}-4< \sqrt{12}+0=\sqrt{12}\)

mà \(\sqrt{12}=\sqrt{4.3}=\sqrt{4}.\sqrt{3}=2\sqrt{3}\)

\(\Rightarrow2\sqrt{3}=\sqrt{5}-4\)

Bạn ơi đề thiếu, bổ sung đi ạ

Tìm x hay tìm a,b vậy bạn??!

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Câu hỏi của Nguyễn Thùy Linh - Toán lớp 9 - Học toán với OnlineMath

vào thóng kê 

k 3 phát như đã hứa nhé 

HHHHHHOOOOCJJJJ TOOOOTS @@

(•‿•)  

\(\sqrt{\frac{1}{2}}+\sqrt{4,5}-\sqrt{12,5}-0,5\sqrt{200}+\sqrt{242}+6\sqrt{1\frac{1}{8}}-\sqrt{24,5}\)

\(=\frac{\sqrt{2}}{2}+\frac{3\sqrt{2}}{2}-\frac{5\sqrt{2}}{2}-5\sqrt{2}+11\sqrt{2}+\frac{9\sqrt{2}}{2}-\frac{7\sqrt{2}}{2}\)

\(=\frac{\sqrt{2}}{2}+6\sqrt{2}\)

\(=\frac{13\sqrt{2}}{2}\)

\(ĐKXĐ:\hept{\begin{cases}\sqrt{x}-1\ne0\\x\ge0\end{cases}\Leftrightarrow}\hept{\begin{cases}x\ne1\\x\ge0\end{cases}}\)

\(B=\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\frac{x-1}{x+\sqrt{x}+1}\)

\(=\left(\frac{2\sqrt{x}+x}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right).\frac{x+\sqrt{x}+1}{x-1}\)

​\(=\left(\frac{2\sqrt{x}+x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right).\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)​

\(=\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)}.\frac{1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\frac{1}{x-1}\)

\(D=\left(\frac{x-2\sqrt{x}}{x-4}-1\right):\left(\frac{4}{x-\sqrt{x}-6}-\frac{\sqrt{x}-2}{3-\sqrt{x}}-\frac{\sqrt{x}-3}{\sqrt{x}+2}\right)\)

\(=\left(\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-1\right):\left(\frac{4-x}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}-2}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}+2}\right)\)

ĐKXĐ:

\(\sqrt{x}\ge0\Rightarrow x\ge0\)

\(\sqrt{x}-2\ne0\Rightarrow\sqrt{x}\ne2\Rightarrow x\ne4\)

\(\sqrt{x}-3\ne0\Rightarrow\sqrt{x}\ne3\Rightarrow x\ne9\)

ĐKXĐ: \(x\ge0;x\ne4;x\ne9\)

\(D=\left(\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-1\right):\left(\frac{4-x}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}-2}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}+2}\right)\)

\(=\left(\frac{\sqrt{x}}{\sqrt{x}+2}-1\right):\left(\frac{4-x}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}-2}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}+2}\right)\)

\(=\frac{\sqrt{x}-\sqrt{x}-2}{\sqrt{x}+2}:\frac{4-x+\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)-(\sqrt{x}-3)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{-2}{\sqrt{x}+2}:\frac{4-x+x-4-x+\sqrt{x}+6}{(\sqrt{x}-3)\left(\sqrt{x}+2\right)}\)

\(=\frac{-2}{\sqrt{x}+2}:\frac{-x+\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{-2}{\sqrt{x}+2}.\frac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}{-\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{2}{\sqrt{x}+2}\)