ta co x+y+3/z=y+z+1/x=x+z+2/y=1/x+y+z, theo tinh chat cua day ti so bang nhau ta co

x+y+3/z=y+z+1/x=x+z+2/y=1/x+y+z=(3+1+2)+2x+2y+2z/z+y+x=6+2(x+y+z)/x+y+z=8

suy ra 1/x+y+z=8 suy ra x+y+z=1/8(1)

ta co x+y+3/z=y+z+1/x=x+z+2/y=8

suy ra x+y+3/z+1=y+z+1/x=x+z+2/y+1

suy ra x+y+z+3/z=y+z+x+1=x+z+y+2/y=9(2)

the (1) vao (2) ta co

1/8+3/z=1/8+1/y=1/8+2/x

suy ra 25/8/z=9/8/y=17/8/x

suy ra z=25/8:8=25/64

y=9/8:8=9/64

x=17/8:8=17/64

nho nhe

Sửa đề: \(\dfrac{x}{x+1}+\dfrac{y}{y+1}+\dfrac{z}{z+1}\ge\dfrac{3}{4}\)

Đặt \(P=\dfrac{x}{x+1}+\dfrac{y}{y+1}+\dfrac{z}{z+1}\)

\(P=\dfrac{x+1}{x+1}-\dfrac{1}{x+1}+\dfrac{y+1}{y+1}-\dfrac{1}{y+1}+\dfrac{z+1}{z+1}-\dfrac{1}{z+1}\)

\(P=1-\dfrac{1}{x+1}+1-\dfrac{1}{y+1}+1-\dfrac{1}{z+1}\)

\(P=3-\left(\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}\right)\)

Ta có:

\(\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}\ge\dfrac{9}{x+y+z+3}\)

\(\Leftrightarrow\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}\ge\dfrac{9}{4}\) ( vì \(x+y+z=1\) )

\(\Rightarrow P\ge3-\dfrac{9}{4}=\dfrac{3}{4}\left(đpcm\right)\)

Dấu "=" xảy ra khi \(x+1=y+1=z+1\)

                               \(\Leftrightarrow x=y=z=\dfrac{1}{3}\)

Vậy \(Max_P=\dfrac{3}{4}\) khi \(x=y=z=\dfrac{1}{3}\)

Ta có : 

      x - y - z = 0

=> 

Có : 

   \(B=\left(1-\frac{z}{x}\right).\left(1-\frac{x}{y}\right).\left(1+\frac{y}{z}\right)\)

  \(B=\left(\frac{x-z}{x}\right).\left(\frac{y-x}{y}\right).\left(\frac{z+y}{z}\right)\)

Thay các biểu thức trong khung trên và B ta có :

 \(B=\frac{y}{x}.\frac{y-\left(y+z\right)}{y}.\frac{x}{z}\)

=> \(B=\frac{y}{x}.\frac{y-y-z}{y}.\frac{x}{z}=\frac{y.\left(-z\right).x}{x.y.z}=-1\)

Vậy B = -1

nha !!!

Ta có: \(x-y-z=0\Rightarrow\hept{\begin{cases}x=z+y\\y=x-z\\-z=y-x\end{cases}}\)

\(B=\left(1-\frac{z}{x}\right).\left(1-\frac{x}{y}\right).\left(1+\frac{y}{z}\right)\)

\(\Rightarrow B=\frac{x-z}{x}.\frac{y-x}{y}.\frac{z+y}{z}\)

\(\Rightarrow B=\frac{y}{x}.\frac{-z}{y}.\frac{x}{z}\)

\(\Rightarrow B=\frac{y.\left(-z\right).x}{x.y.z}=-1\)

Vậy giá trị của biểu thức \(B=-1.\)

1.4m+7n=0

=>4m=-7n

=>mx²-4m=0

=>m(x²-4)=0

=>m=0 hoặc x=2 hoặc x=-2

x + y = 7/12  =>  x = 7/12 - y
y + z = -19/24  =>  z = -19/24 - y
Mà z + x = 1/8  =>  7/12 - y - 19/24 - y = 1/8
=>  2y = 7/12 - 19/24 - 1/8  =>  2y = -1/3
=> y = -1/6

thank

M = x+y/z + x+z/y + y+z/x

M = x+y+z/z + x+y+z/y + x+y+z/x - z/z - y/y - x/x

M = (x+y+z).(1/z + 1/y + 1/x) - 1 - 1 - 1

M = 2020.1/202 - 3

M = 10 - 3 = 7