A = \(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+...+\dfrac{1}{152}\)

=> \(\dfrac{3}{2}\)A = \(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+...+\dfrac{3}{304}\)

= \(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{16.19}\)

= \(1-\dfrac{1}{19}=\dfrac{18}{19}\)

=> A = \(\dfrac{18}{19}:\dfrac{3}{2}=\dfrac{12}{19}\)

Ta có: \(\dfrac{2017}{2018}>\dfrac{2017}{2018+2019}\)

\(\dfrac{2018}{2019}>\dfrac{2018}{2018+2019}\)

=> \(\dfrac{2017}{2018}+\dfrac{2018}{2019}>\dfrac{2017+2018}{2018+2019}\)

=> A > B

1.They asked him,"Do you like to play this game?"

->they asked him if he liked to play that game

2.He said to me"I must finish these works on time"

->He asked me to finish those works on time

3.She asked me"Why do you have to do this work"

->She saked me why I had to do that work

4.He said to me,"Do this test again,please"

->He requested me to do that test again

5.The teacher said to them,"Don't make noise in class"

->The teacher told them not to make noise in class

6.Mary said to me,"Can I borrow you some money?I want to buy this shirt"

->Mary asked me to borrow me some money to buy that shirt

7.They asked him,"Shall we go to the stadium tomorrow?"

->They invited him to go to the stadium the next day

8.She said"I am thinking about my childhood days"

->She said she was thinking about her childhood days

9.The interviewer said to me"why do you want this job?"

->The interviewer asked me why I wanted that job

10."I'm very grateful to you for such a wonderful evening,Nam"->Lan said to Nam she was very grateful to he for such a wonderful evening

11.'Who gave you the money?"->I asked my son who had given him the money

a) \(\dfrac{3}{7}x-\dfrac{2}{3}x=\dfrac{10}{21}\)

<=> \(x\left(\dfrac{3}{7}-\dfrac{2}{3}\right)=\dfrac{10}{21}\)

<=> \(x.\left(-\dfrac{5}{21}\right)=\dfrac{10}{21}\)

<=> \(x=-2\)

b) \(\dfrac{7}{35}:\left(x-\dfrac{1}{3}\right)=-\dfrac{2}{25}\)

<=> \(x-\dfrac{1}{3}=-\dfrac{5}{2}\)

<=> \(x=-\dfrac{13}{6}\)

Đặt \(\dfrac{x}{3}=\dfrac{y}{2}=k\)

=> \(\left\{{}\begin{matrix}x=3k\\y=2k\end{matrix}\right.\)

Do xy² = 96 => 3k.4k² = 96 => 12k³ = 96 => k³ = 8 => k = 2

=> \(\left\{{}\begin{matrix}x=6\\y=4\end{matrix}\right.\)

a) x⁷ + x² + 1

= x⁷ - x + x² + x + 1

= x(x⁶-1) + (x²+x+1)

= x(x³+1)(x-1)(x²+x+1) + (x²+x+1)

= (x²+x+1)(x⁵-x⁴+x²-x+1)

b) (ab+bc+ca)² + (a+b+c)²(a²+b²+c²)

= (ab+bc+ca)² + [(a²+b²+c²) + 2(ab+bc+ca)](a²+b²+c²)

Đặt a²+b²+c² = x ; ab + bc + ca = y, ta có:

y² + (x+2x)x = x² + 2xy + y² = (x+y)²

= (a²+b²+c²+ab+bc+ca)²

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\dfrac{x}{a+2b+c}=\dfrac{y}{2a+b-c}=\dfrac{z}{4a-4b+c}=\dfrac{2y}{4a+2b-2c}=\dfrac{x+2y+z}{a+2b+c+4a+2b-2c+4a-4b+c}=\dfrac{x+2y+z}{9a}\)

\(\dfrac{x}{a+2b+c}=\dfrac{y}{2a+b-c}=\dfrac{z}{4a-4b+c}=\dfrac{2x}{2a+4b+2c}=\dfrac{2x+y-z}{2a+4b+2x+2a+b-c-4a+4b-c}=\dfrac{2x+y+z}{9b}\)

\(\dfrac{x}{a+2b+c}=\dfrac{y}{2a+b-c}=\dfrac{z}{4a-4b+c}=\dfrac{4x}{4a+8b+4c}=\dfrac{4y}{8a+4b-4c}=\dfrac{4x-4y+z}{4a+8b+4c-8a-4b+4c+4a-4b+c}=\dfrac{4x-4y-z}{9c}\)

=> \(\dfrac{x+2y+z}{9a}=\dfrac{2x+y+z}{9b}=\dfrac{4x-4y+z}{9c}\)

=> \(\dfrac{a}{x+2y+z}=\dfrac{b}{2x+y+z}=\dfrac{c}{4x-4y+z}\)

a) y = \(\dfrac{x^2}{\left|x\right|}\)=\(\left\{{}\begin{matrix}x\sim x>0\\-x\sim x< 0\end{matrix}\right.\) ( Dẫu ~ là với nhé :v )

b) y = \(\dfrac{1}{2}\left(3x+\left|x\right|\right)=\left\{{}\begin{matrix}x\sim x< 0\\2x\sim x\ge0\end{matrix}\right.\)

1.a) Từ A + D = 180^o mà A = 3D

=> 4D = 180^o

=> D = 45^o

=> A = 135^o

Từ B + C = 180^o mà B - C = 30^o

=> B = (180^o+30^o):2 = 105^o

=> C = 75^o

2.Có A + D = 180^o mà A = 60^o => D = 120^o

B + C = 180^o mà C = 130^o => B = 50^o