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Plz solve thisif xyz=1, then simplify (1+x+y^-1)^-1 × (1+y+z^-1)^-1 × (1+z+x^-1)^-1plz explain your answer and don't spam​

Answer»

Given that xyz=1

⟹y−1=XZ and ⟹y=(xz)−1 .

The KEY idea is to WRITE the y in terms of x,z .

Now,

1(1+x+y−1)+1(1+y+z−1)+1(1+z+x−1)

=1(1+x+xz)+1(1+(xz)−1+z−1)+1(1+z+x−1)

=1(1+x+xz)+xz(xz+1+x)+x(x+xz+1)

=1(1+x+xz)+xz(1+x+xz)+x(1+x+xz)

=1+x+xz(1+x+xz)

=1

∴1(1+x+y−1)+1(1+y+z−1)+1(1+z+x−1)=1

NOTE : You can select any one variable among x,y,z and write interms of two others.

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