\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt...">
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26 tháng 6 2016

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(\sqrt{6}+\sqrt{3}+\sqrt{2}+1\right)\left(5\sqrt{6}-4\sqrt{3}-3\sqrt{2}+5-2\sqrt{2}-\sqrt{3}\right)\)

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

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

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

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

\(=5.2=10\)

Chúc bạn học tốt và nhớ click cho mình với nhá!

NV
18 tháng 10 2019

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

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

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

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

\(B=\frac{\left(\sqrt{a}-1\right)\left(\sqrt{6}-\sqrt{2}\right)\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{a\left(\sqrt{a}-1\right)\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}=\frac{\sqrt{6}-\sqrt{2}}{a+\sqrt{ab}}\)

\(1.\left(\sqrt{5}-\sqrt{6}\right)^2\)                                                              \(6.\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)\)                  \(2.\left(\sqrt{3}-\sqrt{5}\right)^2\)                                                                \(7.\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)\(3.\left(2\sqrt{2}+\sqrt{3}\right)^2\)                 ...
Đọc tiếp

\(1.\left(\sqrt{5}-\sqrt{6}\right)^2\)                                                              \(6.\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)\)                  

\(2.\left(\sqrt{3}-\sqrt{5}\right)^2\)                                                                \(7.\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)

\(3.\left(2\sqrt{2}+\sqrt{3}\right)^2\)                                                            \(8.\sqrt{\left(5+2\sqrt{6}\right)^2}-\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(4.\left(\sqrt{4}-\sqrt{17}\right)^2\)                                                              \(9.\sqrt{\left(\sqrt{7}-2\right)^2}+\sqrt{\left(\sqrt{7}+2\right)^2}\)

\(5.\sqrt{\left(\sqrt{5}-3\right)^2}\)                                                                  \(10.\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)

3
20 tháng 8 2020

Áp dụng HĐT là đc bạn nhé !! 

20 tháng 8 2020

1. \(\left(\sqrt{5}-\sqrt{6}\right)=\left(\sqrt{5}\right)^2-2\sqrt{5}\sqrt{6}+\left(\sqrt{6}\right)^2=5-2\sqrt{30}+6\)

2. \(\left(\sqrt{3}-\sqrt{5}\right)^2=\left(\sqrt{3}\right)^2-2\cdot\sqrt{3}\cdot\sqrt{5}+\left(\sqrt{5}\right)^2=3-2\sqrt{15}+5\)

3. \(\left(2\sqrt{2}+\sqrt{3}\right)^2=\left(2\sqrt{2}\right)^2+2\cdot2\sqrt{2}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2=8+4\sqrt{6}+3\)

4. \(\left(\sqrt{4}-\sqrt{17}\right)^2=\left(\sqrt{4}\right)^2-2\cdot\sqrt{4}\cdot\sqrt{17}+\left(\sqrt{17}\right)^2=4-4\sqrt{47}+17\)

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

6. \(\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)=\left(2\sqrt{5}\right)^2-\left(\sqrt{7}\right)^2=4\cdot5-7=13\)

7. \(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)=\left(2\sqrt{3}\right)^2-\left(5\sqrt{2}\right)^2=12-50=-38\)

8. \(\sqrt{\left(5+2\sqrt{6}\right)^2}-\sqrt{\left(5-2\sqrt{6}\right)^2}=\left|5+2\sqrt{6}\right|-\left|5-2\sqrt{6}\right|=5+2\sqrt{6}-\left(5-2\sqrt{6}\right)=4\sqrt{6}\)9. \(\sqrt{\left(\sqrt{7}-2\right)^2}+\sqrt{\left(\sqrt{7}+2\right)^2}=\left|\sqrt{7}-2\right|+\left|\sqrt{7}+2\right|=-2+\sqrt{7}+2+\sqrt{7}=2\sqrt{7}\)

10. \(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}=\left|\sqrt{3}+\sqrt{2}\right|+\left|\sqrt{3}-\sqrt{2}\right|=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\)

#em mới lớp 8 nên không chắc lắm ạ :((

7 tháng 8 2018

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

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

\(A=\sqrt{1}\)

\(A=1\)

b)\(B=\left(\frac{\sqrt{x}}{\sqrt{xy}-y}-\frac{\sqrt{y}}{\sqrt{xy}-x}\right).\left(x\sqrt{y}-y\sqrt{x}\right)\)

\(B=\frac{\sqrt{xy}}{\sqrt{xy}-y}x\sqrt{y}+\frac{\sqrt{x}}{\sqrt{xy}-y}y\sqrt{x}+\left(-\frac{\sqrt{y}}{\sqrt{xy}-x}\right)^2x\sqrt{y}+y\sqrt{x}\)

\(B=x\frac{\sqrt{x}}{\sqrt{xy}-y}\sqrt{y}+y\frac{\sqrt{x}}{\sqrt{xy}-y}\sqrt{x}+x\frac{\sqrt{x}}{\sqrt{xy}-x}\sqrt{y}-y\sqrt{x}\frac{\sqrt{y}}{\sqrt{xy}-y}\)

\(B=\frac{-x^{\frac{5}{2}}\sqrt{y}+\sqrt{x}.y^{\frac{5}{2}}}{\left(\sqrt{xy}-y\right)\left(\sqrt{xy}-x\right)}\)

\(B=\frac{\left(\sqrt{x}.y^{\frac{5}{2}}-x^{\frac{5}{2}}\sqrt{y}\right)\left(y+\sqrt{xy}\right)\left(x+\sqrt{xy}\right)}{\left(-y^2+xy\right)\left(-x^2+xy\right)}\)

c) \(C=\sqrt{\left(3-\sqrt{5}\right)^2+\sqrt{6}-2\sqrt{5}}\)

\(C=14-6\sqrt{5}+\sqrt{6}-2\sqrt{5}\)

\(C=14-8\sqrt{5}+\sqrt{6}\)

\(C=\sqrt{14-8\sqrt{5}+\sqrt{6}}\)

25 tháng 3 2019

a,\(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=5\)

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

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

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

\(\Leftrightarrow\sqrt{x-1}-3\le0\left(|A|=-A\Leftrightarrow A\le0\right)\)

\(\Leftrightarrow\sqrt{x-1}\le3\Leftrightarrow0\le x-1\le3^2\Leftrightarrow1\le x\le10\)

Nghiệm của phương trình đã cho là : \(1\le x\le10\)

25 tháng 3 2019

b, \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)=4\)

\(\Leftrightarrow\left[\left(4x+1\right)\left(3x+2\right)\right]\left[\left(12x-1\right)\left(x+1\right)\right]=4\)

\(\Leftrightarrow\left(12x^2+8x+3x+2\right)\left(12x^2+12x-x-1\right)=4\)

\(\Leftrightarrow\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)=4\)

\(\Leftrightarrow\left(12x^2+11x+\frac{1}{2}+\frac{3}{2}\right)\left(12x^2+11x+\frac{1}{2}-\frac{3}{2}\right)=4\)

\(\Leftrightarrow\left(12x^2+11x+\frac{1}{2}\right)^2-\left(\frac{3}{2}\right)^2=4\Leftrightarrow\left(12x^2+11x+\frac{1}{2}\right)^2=4+\frac{9}{4}\)

\(\Leftrightarrow\left(12x^2+11x+\frac{1}{2}\right)^2=\left(\frac{5}{2}\right)^2\Leftrightarrow\orbr{\begin{cases}12x^2+11x+\frac{1}{2}=\frac{5}{2}\\12x^2+11x+\frac{1}{2}=-\frac{5}{2}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}12x^2+11x-2=0\left(1\right)\\12x^2+11x+3=0\left(2\right)\end{cases}}\)

Giải (1)          \(\Delta=121+96=217\)

                      \(x_1=\frac{-11+\sqrt{217}}{24};x_2=\frac{-11-\sqrt{217}}{24}\)

Giải (2)        \(\Delta=121-144=-23< 0\).Phương trình vô nghiệm.

Phương trình có 2 nghiệm phân biệt :

\(x_1=\frac{-11+\sqrt{217}}{24};x_2=\frac{-11-\sqrt{217}}{24}\)

30 tháng 7 2020

- Các ĐKXĐ tự tìm dùm mình hen :)

Ta có : \(D=\left(\frac{5}{x-\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\frac{1}{\sqrt{x}-3}\)

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

=> \(D=\left(\frac{5+\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\right)\left(\sqrt{x}-3\right)\)

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

=> \(D=\left(\frac{1}{\sqrt{x}-3}\right)\left(\sqrt{x}-3\right)=1\)

Ta có : \(E=\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a+1}}{a-2\sqrt{a}+1}\)

=> \(E=\left(\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a+1}}{\left(\sqrt{a}-1\right)^2}\)

=> \(E=\left(\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)

=> \(E=\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)^2}{\sqrt{a}\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}=\frac{\sqrt{a}-1}{\sqrt{a}}\)

( làm đến đây thôi câu còn lại bạn tự làm hen )

Ghét nhất mấy câu viết sai đề b, c sai rất nhiều bạn ới

30 tháng 7 2020

đấy là mình đánh máy tính nên kéo dài hơi nhầm bạn ơi chứ không phải sai đề :))