m là một số vô tỉ

Trả lời:

\(A=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+4\sqrt{3}}}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{5-\sqrt{12+4\sqrt{3}+1}}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{5-2\sqrt{3}-1}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{3-2\sqrt{3}+1}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{\left(\sqrt{3}-1\right)^2}}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{2\sqrt{3+\sqrt{3}-1}}{\sqrt{6}+\sqrt{2}}\)

\(A=\frac{\sqrt{2}.\sqrt{2}.\sqrt{2+\sqrt{3}}}{\sqrt{2}.\left(\sqrt{3}+1\right)}\)

\(A=\frac{\sqrt{2}.\sqrt{4+2\sqrt{3}}}{\sqrt{2}.\left(\sqrt{3}+1\right)}\)

\(A=\frac{\sqrt{2}.\sqrt{3+2\sqrt{3}+1}}{\sqrt{2}.\left(\sqrt{3}+1\right)}\)

\(A=\frac{\sqrt{2}.\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}.\left(\sqrt{3}+1\right)}\)

\(A=\frac{\sqrt{2}.\left(\sqrt{3}+1\right)}{\sqrt{2}.\left(\sqrt{3}+1\right)}\)

\(A=1\)

Câu trên đề sai

\(\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\)

\(=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+4\sqrt{3}}}}}{\sqrt{6}+\sqrt{2}}\)

\(=\frac{2\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{6}+\sqrt{2}}\)

\(=\frac{2\sqrt{2+\sqrt{3}}}{\sqrt{6}+\sqrt{2}}=\sqrt{2}\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{6}+\sqrt{2}}\)

\(=\frac{\sqrt{2}\left(\sqrt{3}+1\right)}{\sqrt{6}+\sqrt{2}}=1\)

Vậy nó là số nguyên

Lớn hơn hoặc bằng đấy

Giả sử a = b = 2 thì VT = 4 < VP = 16

Nhiêu đây là thấy đề sai rồi

Trả lời 

\(\frac{3\sqrt{2}+2\sqrt{2}}{\sqrt{3}+\sqrt{2}}+\frac{\sqrt{6}+6}{\sqrt{6}+1}\)

\(=\frac{\sqrt{2}.\left(3+2\right)}{\sqrt{3}+\sqrt{2}}+\frac{6+\sqrt{6}}{\sqrt{6}+1}\)

\(=\frac{5\sqrt{2}}{\sqrt{3}+\sqrt{2}}+\frac{\sqrt{6}.\left(\sqrt{6}+1\right)}{\sqrt{6}+1}\)

\(=\frac{5\sqrt{2}.\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right)}+\sqrt{6}\)

\(=\frac{5\sqrt{6}-5.2}{3-2}+\sqrt{6}\)

\(=\frac{5\sqrt{6}-10}{1}+\sqrt{6}\)

\(=5\sqrt{6}-10+\sqrt{6}\)

\(=6\sqrt{6}-10\)

Trả lời:

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-12\sqrt{5}+9}}}\)

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

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

\(A=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{5-2\sqrt{5}+1}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{5}+1}\)

\(A=\sqrt{1}\)

\(A=1\)

\(B=\frac{\left(5+2\sqrt{6}\right).\left(49-20\sqrt{6}\right).\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(3+2\sqrt{6}+2\right).\left(49-20\sqrt{6}\right).\sqrt{3-2\sqrt{6}+2}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right)^2.\left(49-20\sqrt{6}\right).\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right)^2.\left(49-20\sqrt{6}\right).\left(\sqrt{3}-\sqrt{2}\right)}{9\sqrt{33}-11\sqrt{2}}\)

\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right).\left(49-20\sqrt{6}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{\left(3-2\right).\left(49\sqrt{3}-60\sqrt{2}+49\sqrt{2}-40\sqrt{3}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=\frac{1.\left(9\sqrt{3}-11\sqrt{2}\right)}{9\sqrt{3}-11\sqrt{2}}\)

\(B=1\)

a) Ta có: \(\sqrt{29-12\sqrt{5}}=\sqrt{20-12\sqrt{5}+9}=\sqrt{\left(2\sqrt{5}-3\right)^2}\)

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

\(\Rightarrow\sqrt{3-\sqrt{29-12\sqrt{5}}}=\sqrt{3-\left(2\sqrt{5}-3\right)}=\sqrt{3-2\sqrt{5}+3}\)

\(=\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-1\right)^2}\)

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

\(\Leftrightarrow A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}\)

\(=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\)( đpcm )

Đặt \(x^2=t\left(t\ge0\right)\)

\(\Leftrightarrow t^2-16t+32=0\)

\(\Delta=\left(-16\right)^2-4.32=256-128=128>0\)

\(t_1=\frac{16-\sqrt{128}}{2}=8-4\sqrt{2};t_2=\frac{16+\sqrt{128}}{2}=8+4\sqrt{2}\)

Theo bài ra ta có : 

\(x_0=\sqrt{2+\sqrt{2+\sqrt{3}}}-\sqrt{6-3\sqrt{2+\sqrt{3}}}\)

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

tịt lun, cái pt căn này chill quá 

 ๖²⁴ʱ๖ۣۜTɦủү❄吻༉ Mơn Bạn nha .

P/s : làm nháp thử mn sửa giúp nha ( thực ra em cũng chả hiểu cái gì cả T_T )

Ta có :

\(\left(x_0\right)^2=8-2\sqrt{2+\sqrt{3}}-2\sqrt{3\left(2-\sqrt{3}\right)}\)

\(\Rightarrow\left(\frac{8-\left(x_0\right)^2}{2}\right)^2=2+\sqrt{3}+3\left(2-\sqrt{3}\right)+2\sqrt{3\left(4-3\right)}=8\)

\(\Rightarrow64-16\left(x_0\right)^2+\left(x_0\right)^4=32\)

\(\Rightarrow\left(x_0\right)^4-16\left(x_0\right)^2+32=0\left(đpcm\right)\)

ta có \(8-2\sqrt{3}+2\sqrt{3}=\left(2\cdot\sqrt{2}\right)^2\)

\(\Leftrightarrow\left(2+\sqrt{3}\right)+\left(6-3\sqrt{3}\right)+2\sqrt{\left(2+\sqrt{3}\right)\left(6-3\sqrt{3}\right)}=\left(2\cdot\sqrt{2}\right)^2\)

\(\Leftrightarrow\left(\sqrt{2+\sqrt{3}}+\sqrt{6-3\sqrt{3}}\right)^2=\left(2\cdot\sqrt{2}\right)^2\)

\(\Leftrightarrow\sqrt{2+\sqrt{3}}+\sqrt{6-3\sqrt{3}}=2\sqrt{2}\)

\(\Leftrightarrow8-2\sqrt{2+\sqrt{3}}-2\sqrt{\left(2+\sqrt{2+\sqrt{3}}\right)\left(6-\sqrt{2+\sqrt{3}}\right)}=8-4\sqrt{2}\)

\(\Leftrightarrow\left(\sqrt{2+\sqrt{2+\sqrt{3}}}-\sqrt{6-3\sqrt{2+\sqrt{3}}}\right)^2=8-4\sqrt{2}\)

\(\Leftrightarrow x_0^2=8-4\sqrt{2}\)

\(\Leftrightarrow x_0^2-\left(8-4\sqrt{2}\right)=0\)

\(\Leftrightarrow\left[x_0^2-\left(8-4\sqrt{2}\right)\right]\left[x_0^2-\left(8+4\sqrt{2}\right)\right]=0\)

\(\Leftrightarrow x_0^4-16x_0^2+32=0\)