a) Vì x <  3 => | x - 3 | = - ( x - 3 )

 => - ( x - 3 ) + x - 5

=>  -x + 3 + x - 5

=> ( -x + x ) +( 3 - 5)

=>     0         + ( -2 )

=>           -2

b)Vì x lớn hơn hoặc bằng -2 => |2 + x| = x + 2

=> ( x + 2 ) - ( x + 1)

=  x + 2 - x - 1

= ( x - x ) + ( 2 - 1)

=     0           + 1

=      1

Câu c tương tự nhé

làm cho mk câu c vs Nguyễn Thảo Nguyên ơi

a) /x-2/ nhỏ hơn hoặc bằng 2

vì /a/ \(\ge\)0

mà /x-2/\(\le\)2

\(\Rightarrow\)/x-2/={0;1;2}

Nếu /x-2/=0

   x-2 =0

\(\Rightarrow\)x=2

Nếu /x-2/=1

   x-2  =1

\(\Rightarrow\)x=3

Nếu /x-2/=2

   x-2 =2

\(\Rightarrow\)x=4

Vì x\(\in\)Z nên x={2;3;4}

b) /x-3/ nhỏ hơn hoặc bằng 0

Vì /a/\(\ge\)0

mà /x-3/\(\le\)0

nên /x-3/=0

        x-3 =0

    \(\Rightarrow\)x=3

1) Giải theo cách lớp 8 nhé: 
Áp dụng BĐT (a + b)² >= 4ab (với a,b là các số không âm). Dấu "=" xảy ra khi a = b. C/m đơn giản thôi, bạn chuyển vế đưa về hằng đẳng thức đúng. 
(x + y)² >= 4xy 
(y + z)² >= 4yz 
(x + z)² >= 4xz 
Nhân theo vế 3 BĐT trên có: (x + y)²(y + z)²(x + z)² >= 64x²y²z² 
=> (x + y)(y + z)(z + x) >= 8xyz (vì x,y,z >= 0) 
2) ĐK để các phân thức có nghĩa: a + b; b + c; c +a khác 0. 
Ta có: a²/(a +b) + b²/(b + c) + c²/(c + a) = b²/(a +b) + c²/(b + c) + a²/(c + a) (*) 
<=> a²/(a +b) + b²/(b + c) + c²/(c + a) - b²/(a +b) - c²/(b + c) - a²/(c + a) = 0 
<=> (a² - b²)/(a + b) + (b² - c²)/(b + c) + (c² - a²)/(c + a) = 0 
<=> (a - b)(a + b)/(a + b) + (b - c)(b + c)/(b + c) + (c - a)(c + a)/(c + a) = 0 
<=> a - b + b - c + c - a = 0 
<=> 0 = 0 (1) 

Hơi tắt nhá

a) Đặt \(\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|=A\)

\(\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\ge0\forall x;y;z\)

mà A\(\le0\)

​​\(\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\)​ phải bằng 0 đê thỏa mãn điều kiện

\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{9}{2}\right|=0\\\left|y+\dfrac{4}{3}\right|=0\\\left|z+\dfrac{7}{2}\right|=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{9}{2}\\y=-\dfrac{4}{3}\\z=-\dfrac{7}{2}\end{matrix}\right.\)

Vậy....

b;c)I hệt câu a nên làm tương tự nhá

d)

Hơi tắt nhá

a) Đặt \(\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{1}{5}\right|+\left|x+y+z\right|=B\)

B=\(\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{1}{5}\right|+\left|x+y+z\right|=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{3}{4}\right|=0\\\left|y-\dfrac{1}{5}\right|=0\\\left|x+y+z\right|=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{4}\\y=\dfrac{1}{5}\\x+y+z=0\end{matrix}\right.\)

Thay ra ta tính đc :\(z=-\dfrac{11}{20}\)

Vậy....

\(\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\le0\)

\(\left\{{}\begin{matrix}\left|x+\dfrac{9}{2}\right|\ge0\\\left|y+\dfrac{4}{3}\right|\ge0\\\left|z+\dfrac{7}{2}\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\ge0\\\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|\le0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{9}{2}\right|=0\Rightarrow x=-\dfrac{9}{2}\\\left|y+\dfrac{4}{3}\right|=0\Rightarrow y=-\dfrac{4}{3}\\\left|z+\dfrac{7}{2}\right|=0\Rightarrow z=-\dfrac{7}{2}\end{matrix}\right.\)

\(\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{2}{5}\right|+\left|z+\dfrac{1}{2}\right|\le0\)

\(\left\{{}\begin{matrix}\left|x+\dfrac{3}{4}\right|\ge0\\\left|y-\dfrac{2}{5}\right|\ge0\\\left|z+\dfrac{1}{2}\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{2}{5}\right|+\left|z+\dfrac{1}{2}\right|\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{2}{5}\right|+\left|z+\dfrac{1}{2}\right|\ge0\\\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{2}{5}\right|+\left|z+\dfrac{1}{2}\right|\le0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{2}{5}\right|+\left|z+\dfrac{1}{2}\right|=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+\dfrac{3}{4}\right|=0\Rightarrow x=-\dfrac{3}{4}\\\left|y-\dfrac{2}{5}\right|=0\Rightarrow y=\dfrac{2}{5}\\\left|z+\dfrac{1}{2}\right|=0\Rightarrow z=-\dfrac{1}{2}\end{matrix}\right.\)

\(\left|x+\dfrac{19}{5}\right|+\left|y+\dfrac{1890}{1975}\right|+\left|z-2004\right|=0\)

\(\left\{{}\begin{matrix}\left|x+\dfrac{19}{5}\right|\ge0\\ \left|y+\dfrac{1980}{1975}\right|\ge0\\\left|z-2004\right|\ge0\end{matrix}\right.\)

\(\left|x+\dfrac{19}{5}\right|+\left|y+\dfrac{1980}{1975}\right|+\left|z-2004\right|\ge0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left|x+\dfrac{19}{5}\right|=0\Rightarrow x=-\dfrac{19}{5}\\ \left|y+\dfrac{1980}{1975}\right|=0\Rightarrow y=-\dfrac{1980}{1975}\\\left|z-2004\right|=0\Rightarrow z=2004\end{matrix}\right.\)

\(\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{1}{5}\right|+\left|x+y+z\right|=0\)

\(\left\{{}\begin{matrix}\left|x+\dfrac{3}{4}\right|\ge0\\ \left|y-\dfrac{1}{5}\right|\ge0\\\left|x+y+z\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{3}{4}\right|+\left|y-\dfrac{1}{5}\right|+\left|x+y+z\right|\ge0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left|x+\dfrac{3}{4}\right|=0\Rightarrow x=-\dfrac{3}{4}\\\left|y-\dfrac{1}{5}\right|=0\Rightarrow y=\dfrac{1}{5}\\\left|x+y+z\right|=0\Rightarrow z+-\dfrac{11}{20}=0\Rightarrow z=\dfrac{11}{20}\end{matrix}\right.\)

Đặt \(\left|x+\dfrac{9}{2}\right|+\left|y+\dfrac{4}{3}\right|+\left|z+\dfrac{7}{2}\right|=A\)

\(\Rightarrow A\ge0\)

Mà ĐK đề là \(A\le0\)

\(\Rightarrow A=0\)

\(\left[{}\begin{matrix}\left|x+\dfrac{3}{4}=0\right|\Rightarrow x=-\dfrac{3}{4}\\\left|y-\dfrac{2}{5}=0\right|\Rightarrow y=\dfrac{2}{5}\\\left|z+\dfrac{1}{2}=0\right|\Rightarrow z=-\dfrac{1}{2}\end{matrix}\right.\)

Các câu còn lại tương tự nhé

a) x \(\in\)B(3) = {0;3;6;9;12;15;18;21;24...;63;66;...}

Mà \(21\le x\le65\)=> x \(\in\){21;24;...;63}

b) x \(⋮\)17 => x \(\in\)B(17) = {0;17;34;51;68;...}

Mà \(0\le x\le60\)=> x \(\in\){0;17;34;51}

c) x \(\in\)Ư(30) = {1;2;3;5;6;10;15;30}

Mà \(x\ge0\)=> x \(\in\){1;2;3;5;6;10;15;30}

d) \(x⋮7\)=> x \(\in\)B(7) = {0;7;14;21;28;35;42;49;56;...}

Mà \(x\le50\)thì loại bỏ số 56 ta được các số còn lại

Chịu 🐻 

-21/3 bé hơn hoặc =x bé hơn hoặc =2

\(a,\left(x-1\right)\left(x+2\right)\le0\)

th1 : 

\(\hept{\begin{cases}x-1\ge0\\x+2\le0\end{cases}\Rightarrow\hept{\begin{cases}x\ge1\\x\le-2\end{cases}}\Rightarrow loai}\)

th2 : 

\(\hept{\begin{cases}x-1\le0\\x+2\ge0\end{cases}\Rightarrow\hept{\begin{cases}x\le1\\x\ge-2\end{cases}\Rightarrow}-2\le x\le1}\)

\(b,\left(x-5\right)\left(3-x\right)>0\)

th1 : 

\(\hept{\begin{cases}x-5>0\\3-x>0\end{cases}\Rightarrow\hept{\begin{cases}x>5\\x< 3\end{cases}\Rightarrow}loai}\)

th2 : 

\(\hept{\begin{cases}x-5< 0\\3-x< 0\end{cases}\Rightarrow\hept{\begin{cases}x< 5\\x>3\end{cases}\Rightarrow}3< x< 5}\)

c tương tự nha em