Question

cho x,y,z thỏa mãn xyz=1.  cm:  1/ xy+x+1  +1/ yz+y+1  +1/ xyz+yz+y  =1

Answer 1

Từ xyz=1

=>\(\frac{1}{xy+x+1}+\frac{1}{yz+y+1}+\frac{1}{xyz+zx+z}=\frac{z}{xyz+xz+z}+\frac{xz}{xyz^2+xyz+xz}+\frac{1}{xyz+zx+z}\)=\(\frac{z}{1+zx+z}+\frac{xz}{1+z+xz}+\frac{1}{1+xz+z}=1\left(đpcm\right)\)

Answer 2

ác mộng trả lời sai rồi

Answer 3

Ta có:1/1+x+xy + 1/1+y+yz +1/1+z+xz= xyz/ xyz+x+xy +1/1+y+yz + xyz/xyz+z+xz =yz/yz+y+1 + 1/ yz+y+1 +xy/xy+x+1 =yz+1/yz+y+1 +xy.xyz/xy+x+xyz =yz+1/yz+y+1 +xy^2z/y+yz+1 =yz+1+y/yz+y+1 =1(đpcm)

Answer 4

ác mộng đúng mà