Question

[Anh Mai]

Biết x.y.z=1

Tính A= x/x.y+x+1 +y/y.z+y+1 + z/z.x+z+1

Answer 1

[Akai Haruma]

Lời giải:

Ta có:

\(A=\frac{x}{xy+x+1}+\frac{y}{yz+y+1}+\frac{z}{zx+z+1}\)

\(A=\frac{xz}{xyz+xz+z}+\frac{y.xz}{yz.xz+y.xz+xz}+\frac{z}{zx+z+1}\)

\(A=\frac{xz}{1+xz+z}+\frac{1}{z+1+xz}+\frac{z}{xz+z+1}\) (thay \(xyz=1\) )

\(A=\frac{xz+1+z}{1+xz+z}=1\)