Question

if
xyz =1
Prove that
(1+x+y^-1)^-1+(1+y+z^-1)^-1 + (1+z+x^-1)^-1 = 1​

Answer 1

Answer:

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Step-by-step explanation:

-- If xyz = 1, then how can I prove that (1+x+y−1)−1+(1+y+z−1)−1+(1+z+x−1)−1=1 ?

If xyz = 1, then how can I prove that (1+x+y−1)−1+(1+y+z−1)−1+(1+z+x−1)−1=1 ?Business laptop at Rs. 899* per month.

If xyz = 1, then how can I prove that (1+x+y−1)−1+(1+y+z−1)−1+(1+z+x−1)−1=1 ?Business laptop at Rs. 899* per month.Given that xyz=1

If xyz = 1, then how can I prove that (1+x+y−1)−1+(1+y+z−1)−1+(1+z+x−1)−1=1 ?Business laptop at Rs. 899* per month.Given that xyz=1 ⟹y−1=xz and ⟹y=(xz)−1 .

-- The key idea is to write the y in terms of x,z .

The key idea is to write the y in terms of x,z .Now,

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)

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)

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

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

=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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