a: \(3x-\left|2x+1\right|=2\)

\(\Leftrightarrow\left|2x+1\right|=3x-2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x-2\right)^2-\left(2x+1\right)^2=0\\x>=\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(3x-2-2x-1\right)\left(3x-2+2x+1\right)=0\\x>=\dfrac{2}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)\left(5x-1\right)=0\\x>=\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow x=3\)

e: Ta có: \(2n-3⋮n+1\)

\(\Leftrightarrow2n+2-5⋮n+1\)

\(\Leftrightarrow n+1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{0;-2;4;-6\right\}\)

Câu 2:A= 75.(42004+42003+.....+42+4+1)+25=75.|(4²⁰⁰⁵-1):3+25=25.(4²⁰⁰⁵-1+1)=25.4²⁰⁰⁵chia hết 100

Suy ra A chia hết cho 100

CHÚC BẠN HỌC TỐT NHÉ !!!!!!!!!

Câu 1:

Vậy \(M=4;M=-4.\)

Chúc bạn học tốt!

A) \(\frac{a}{b}=\frac{c}{d}=t\Rightarrow a=bt,c=dt\)

\(\frac{a}{a+b}=\frac{bt}{bt+b}=\frac{t}{t+1},\frac{c}{c+d}=\frac{dt}{dt+d}=\frac{t}{t+1}\)

suy ra đpcm. 

\(\frac{a-b}{c-d}=\frac{bt-b}{dt-d}=\frac{b}{d},\frac{a+b}{c+d}=\frac{bt+b}{dt+d}=\frac{b}{d}\)

suy ra đpcm. 

B) \(\frac{a+3c}{b+3d}=\frac{a+c}{b+d}=\frac{\left(a+3c\right)-\left(a+c\right)}{\left(b+3d\right)-\left(b+d\right)}=\frac{2c}{2d}=\frac{c}{d}\)

\(\frac{a+3c}{b+3d}=\frac{a+c}{b+d}=\frac{\left(a+3c\right)-3\left(a+c\right)}{\left(b+3d\right)-3\left(b+d\right)}=\frac{-2a}{-2b}=\frac{a}{b}\)

suy ra đpcm. 

Ta có :

M = ( a + b + c - d ) + ( a + b - c + d ) + ( a - b + c + d ) + ( -a + b + c + d )

= a + b + c - d + a + b - c + d + a - b + c + d - a + b + c + d 

= ( a + a + a - a ) + ( b + b - b + b ) + ( c - c + c + c ) + ( - d + d + d + d )

= 2a + 2b + 2c + 2d 

= 2 . ( a + b + c + d )

Thay a = 1 , b = 10 , c = 100 và d = 1000 vào biểu thức M có :

M = 2 .( 1 + 10 + 100 + 1000 )

M = 2 . 1111

M = 2222 

Vậy M = 2222 khi a = 1 , b = 10 , c = 100 và d = 1000 .

Học tốt

\(M=\left(a+b+c-d\right)+\left(a+b-c+d\right)+\left(a-b+c+d\right)+\left(-a+b+c+d\right)\)

\(=a+b+c-d+a+b-c+d+a-b+c+d-a+b+c+d\)

\(=\left(a+b+c+d\right).3-\left(a+b+c+d\right)=2\left(a+b+c+d\right)\)

\(=2\left(1+10+100+1000\right)=2.1111=2222\)

\(M=\left(a+b+c-d\right)+\left(a+b-c+d\right)+\left(a-b+c+d\right)+\left(-a+b+c+d\right)\)

\(=a+b+c-d+a+b-c+d+a-b+c+d-a+b+c+d\)

\(=2a+2b+2c+2d\)

Thay a = 1 ; b = 10 ; c = 100 ; d = 1000

\(2.1+2.10+2.100+2.1000=2+20+200+2000\)

\(=2222\)

 a+b+c+d=0 
=>a+b=-(c+d) 
=> (a+b)^3=-(c+d)^3 
=> a^3+b^3+3ab(a+b)=-c^3-d^3-3cd(c+d) 
=> a^3+b^3+c^3+d^3=-3ab(a+b)-3cd(c+d) 
=> a^3+b^3+c^3+d^3=3ab(c+d)-3cd(c+d) ( vi a+b = - (c+d)) 
==> a^3 +b^^3+c^3+d^3==3(c+d)(ab-cd) (đpcm)

hey you, còn câu b,c?

ở đây có ai thích sơn tùng không ?