\(a,\frac{1}{3}+\frac{1}{6}+x=\frac{3}{4}\)                                  \(b,\frac{1}{2}+\frac{1}{3}-x=\frac{2}{3}\)                  \(c,\frac{2}{3}\cdot\frac{3}{4}\cdot x=\frac{2}{5}\)       

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

\(\frac{1}{2}+x=\frac{3}{4}\)                                                \(\frac{5}{6}-x=\frac{2}{3}\)                                   \(\frac{1}{2}\cdot x=\frac{2}{5}\)

\(x=\frac{3}{4}-\frac{1}{2}\)                                                \(x=\frac{5}{6}-\frac{2}{3}\)                                    \(x=\frac{2}{5}:\frac{1}{2}\)

\(x=\frac{1}{4}\)                                                          \(x=\frac{1}{6}\)                                                    \(x=\frac{4}{5}\)

\(d,x:\left(\frac{1}{4}:\frac{1}{2}\right)=\frac{2}{3}\)     \(e,\frac{1}{3}:\frac{1}{2}:x=\frac{3}{4}\)

\(x:\frac{1}{2}=\frac{2}{3}\)                            \(\frac{1}{3}:\frac{1}{2}=\frac{3}{4}\cdot x\)

\(x=\frac{2}{3}\cdot\frac{1}{2}\)                   \(\frac{2}{3}=\frac{3}{4}\cdot x\)

\(x=\frac{1}{3}\)                              \(x=\frac{2}{3}:\frac{3}{4}\)

                                                     \(x=\frac{8}{9}\)

a) 1/3 + 1/6 +x = 3/4                                      b) 1/2 + 1/3 - x = 2/3

                                                                                  5/6  -  x = 2/3

                                                                                           x   =5/6 -2/3

                                                                                           x  =  1/6

           1/2+ x    =3/4

                   x    = 3/4 -1/2

                   x    =  1/4

1, We find playing table tennis very unteresting because we can meet and firends with interesting people .

2, My brother and I have the same hobby 

3, I love playing outboors in my garden to plant flowers and vegetables

4, My father s rides his bike in the park at the weekend

5,Tom and peter water acctivities and they go swimming , play water polo and sury tegether a lot 

6, My hobby is collepling books because I love reading whenever I have time

7,Why don t you go jogging beacause it can help you keep fit ?

1, We ......find..........playing table tennis very unteresting because we can meet and firends with interesting people .

2, My brother and I .......have.........the same hobby 

3, I love ....playing...........outboors in my garden to plant flowers and vegetables

4, My father s ....riding...............his bike in the park at the weekend

5,Tom and peter water .......activitives............and they go swimming , play water polo and sury tegether a lot 

6, My hobby is collepling ......comic..book.............because I love reading whenever I have time

7,Why don t you .......go.......jogging beacause it can help you keep fit ?

1/x+1/y = 1/5

=>(x+y)/xy = 1/5

=> 5x+5y = xy

=> 5x - xy + 5y = 0

=> x(5 - y) +5y = 0 

=> x(5 - y) +5y - 25 = -25

=> x(5 - y) - 5(5 - y) = -25

=> (x - 5)(5 - y) = -25

=> (x - 5)(y - 5) = 25

Ta có: \(VT-VP=\frac{\left(y-x\right)^2\left(xy-1\right)}{\left(1+x^2\right)\left(1+y^2\right)\left(1+xy\right)}\ge0\)(đúng với \(xy\ge1\))

Đẳng thức xảy ra khi a = b = 1

Dấu ở giữa là cộng chứ nhỉ??

Đặt \(y=\sqrt[3]{a+\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}};z=\sqrt[3]{a-\frac{a+1}{3}\sqrt{\frac{8a-1}{3}}}\)

\(\Rightarrow\hept{\begin{cases}y^3+z^3=2a\\yz=\sqrt[3]{a^2-\frac{\left(a+1\right)^2\left(8a-1\right)}{27}}\\y+z=x\end{cases}=\sqrt[3]{\frac{27a^2-\left(8a^3+15a^2+6a-1\right)}{27}}=\sqrt[3]{\frac{\left(1-2a\right)^3}{27}}=\frac{1-2a}{3}}\)

Thay vào ta được:

\(x^3=\left(y+z\right)^3=y^3+z^3+3yz\left(y+z\right)\)\(=2a+3\frac{1-2a}{3}x=2a+\left(1-2a\right)x\)

\(\Leftrightarrow x^3-\left(1-2a\right)x-2a=0\)

\(\Leftrightarrow x^3-x+2ax-2a=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2+2a+x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x^2+2a+x=0\end{cases}}\)

Đến đây thì có lẽ là sẽ cm được \(x^2+2a+x>0\), mình chưa tìm ra cách cm.

KL : \(x=1\inℤ\)

Ta có: \(\frac{a}{b+c}=\frac{b}{a+c}=\frac{c}{a+b}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{b+c}=\frac{b}{a+c}=\frac{c}{a+b}=\frac{a+b+c}{b+c+a+c+a+b}=\frac{a+b+c}{2\left(a+b+c\right)}=\frac{1}{2}\)

Suy ra:

 \(\frac{a}{b+c}=\frac{1}{2}\Rightarrow a=\frac{b+c}{2}=\frac{1}{2}\times\left(b+c\right)\)

\(\frac{b}{a+c}=\frac{1}{2}\Rightarrow b=\frac{a+c}{2}=\frac{1}{2}\times\left(a+c\right)\)

\(\frac{c}{a+b}=\frac{1}{2}\Rightarrow c=\frac{a+b}{2}=\frac{1}{2}\times\left(a+b\right)\)

Thay  \(a=\frac{1}{2}\times\left(b+c\right)\);  \(b=\frac{1}{2}\times\left(a+c\right)\); \(c=\frac{1}{2}\times\left(a+b\right)\) vào P ta được:

\(\frac{b+c}{\frac{1}{2}\times\left(b+c\right)}+\frac{c+a}{\frac{1}{2}\times\left(a+c\right)}+\frac{a+b}{\frac{1}{2}\times\left(a+b\right)}\)

\(=\frac{\text{ }1\text{ }}{\frac{1}{2}}+\frac{1}{\frac{1}{2}}+\frac{1}{\frac{1}{2}}\)

\(=2+2+2=6\)

Vậy giá trị của P  là 6

1. large/ a/ Huong/ has/ with/ decorations/ lot/ a/ beautiful/on/ room/the/ of/ walls.

Huong has a large room with a lot of beautiful decorations on the walls

2. is/ hard-working/ Sue/ student/ a/ and/reads/ books/ a/ lot/ she/ of/every month.

Sue is a hard - working student and she reads a lot of books every month

3. She/ the/ paripating/ is/ in/ sports/ of/ school/ next/ club/ semester./ the

She is paripating in the sports semester club of the next school 

( Câu 4 giống hệt câu 3)

5. Lam/ lives/ near/ so/ his/goes/ school/ school/walk/ he/ to/ by.

Lam lives near his school , so he goes to school by walk.

\(\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=6abc\)

\(\Leftrightarrow2\left(a^2+b^2+c^2-ab-bc-ca\right)=6abc\)

\(\Leftrightarrow a^2+b^2+c^2-ab-bc-ca=3abc\)

Đến đây ta chỉ cần chứng minh \(a^2+b^2+c^2-ab-bc-ca=a^3+b^3+c^3\)

Nhưng rõ ràng: \(a^3+b^3+c^3=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\ne a^2+b^2+c^2-ab-bc-ca\)

     KL : Đề sai.

Gọi số đó là A5 \(\Rightarrow\)Số mới là A. Theo đề bài ta có:

A5 - A = 1805

A x 10 + 5 - A = 1805

A x (10 - 1) = 1805 - 5

A x 9 = 1800

A = 1800 : 9 = 200

Vậy số cần tìm là 2005.