my mother (Travel)        will travel          to ha long bay next week 

mai and hoa (not fly) Will not fly           their kites tomorrow 

my mother will travel to ha long bay next week 

mai and hoa won't fly their kites tomorrow 

_Tử yên_

\(y\left(x+y\right)-x-y=y\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(y-1\right)\)

y.( x + y ) - x - y

= y.( x + y ) - ( x + y )

= ( x + y ).( y - 1 )

tui

1m52

they did                         their home work yesterday 

he did not clean)                   the floor 2 days ago 

- They did their homework yesterday.

- He didn't clean the floor 2 days ago

a² + b² = ab + ba

\(\Leftrightarrow\)a² + b² = 2ab

\(\Leftrightarrow\)a² - 2ab + b² = 0

\(\Leftrightarrow\) ( a - b )²  = 0

\(\Leftrightarrow\) a - b =0

\(\Leftrightarrow\) a = b   ( đpcm )

#)Giải :

\(a^2+b^2=ab+ba\)

\(\Rightarrow2a^2+2b^2-2ab-2ba=0\)

\(\Rightarrow\left(a-b\right)^2+\left(a-b\right)^2=0\)

\(\Rightarrow2\left(a-b\right)^2=0\)

\(\Rightarrow a-b=0\Rightarrow a=b\)

\(\Rightarrow a=b\)

P/s : Mình nhớ đã đc làm một bài giống thế này ở đâu rùi nhỉ ...

ta có:

\(x:\frac{9}{14}=\frac{7}{3}:x\)

\(\Rightarrow\frac{14x}{9}=\frac{7}{3x}\)

\(\Rightarrow42x^2=63\)

\(\Rightarrow x^2=\frac{3}{2}\)

\(\Rightarrow x=\sqrt{\frac{3}{2}}\)

chúc bn hok tốt

\(x:\frac{9}{14}=\frac{7}{3}:x\)

\(\Leftrightarrow\)\(\frac{14x}{9}=\frac{7}{3x}\)

\(\Leftrightarrow\)\(42x^2=63\)

\(\Leftrightarrow\) x² = \(\frac{63}{42}\)

\(\Leftrightarrow\)\(x=\sqrt{\frac{63}{42}}\)

1) She isn't cooking at the moment.

2) Mary didn't watch a film on TV last night.

- She isn't cooking at the moment.

- Mary watched a film on TV last night

n là số tự nhiên nên n có 3 dạng : \(3k+1;3h+2;3l\left(k;h;l\in N\right)\)

\(2005\equiv1\left(mod3\right)\Rightarrow2005^n\equiv1\left(mod3\right)\)=> \(2005^n\)luôn chia 3 dư 1 với mọi số tự nhiên n

+>\(n=3k:n^{2005}⋮3;2005.n⋮3\Rightarrow2005^n+n^{2005}+2005.n⋮3\)dư 1 ( loại )

+>\(n=3k+1:n\equiv1\left(mod3\right)\Leftrightarrow n^{2005}\equiv1\left(mod3\right);2005\equiv1\left(mod3\right)\Leftrightarrow2005.n\equiv1.1=1\left(mod3\right)\)

\(\Rightarrow2005^n+n^{2005}+2005.n\equiv1+1+1=3\left(mod3\right);3⋮3\Rightarrow A⋮3\)( hợp lý -> chọn )

+>\(n=3k+2\Rightarrow n\equiv-1\left(mod3\right)\Leftrightarrow n^{2005}\equiv-1\left(mod3\right);2005\equiv1\left(mod3\right)\Rightarrow2005.n\equiv1.-1=-1\left(mod3\right)\)

\(\Rightarrow2005^n+n^{2005}+2005.n\equiv1+\left(-1\right)+\left(-1\right)=-1\left(mod3\right)\Leftrightarrow A⋮̸3\)( loại )

Vậy n là tất cả các số tự nhiên chia 3 dư 1.

Đỗ Đức Lợi làm thiếu rồi :))

\(A=2005^n+n^{2005}+2005.n⋮3\)

Ta có \(2005\)ko chia hết 3 vì 2005 chia 3 dư 1

=>2005ⁿ=3k+1(k\(\in N\))

Xét +) n=3k ta có A =2005ⁿ+n²⁰⁰⁵.n

A=(3k+1+3k+3k):3 dư 1 

=> loại n=3k

+)n=3k+1 ta có A=3k+1+3k+1+3k+1

A=9k+3

A=3(k+1) \(⋮\)3

+)n=3 k+2 Ta có :

A=3k+1+3k+2+3k+2

A=9k +5 :3 dư 2

=>n=3k+2 ( loại )

Với n=3k+1 thì A=3(k+1) chia hết cho 3

a) \(\frac{7}{23}+\frac{4}{17}-\frac{7}{23}+\frac{13}{14}\)

= \(\left(\frac{7}{23}-\frac{7}{23}\right)+\left(\frac{4}{17}+\frac{13}{14}\right)\)

= \(\frac{277}{238}\)

b) \(19\frac{1}{4}.\frac{7}{12}-15\frac{1}{4}.\frac{7}{12}\)

= \(\left(19\frac{1}{4}-15\frac{1}{4}\right).\frac{7}{12}\)

= \(4.\frac{7}{12}\)

= \(\frac{7}{3}\)

c) \(\left(\frac{5}{6}-\frac{3}{-4}\right)\left(\frac{2}{3}-1\right)\)

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

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

= \(\frac{5}{9}-\frac{5}{6}+\frac{1}{2}-\frac{3}{4}\)

= \(\frac{2}{9}-\frac{3}{4}=-\frac{19}{36}\)