Question

if you know then you will solve
I will mark brainliest for correct solution ​

Answer 1

Answer:

•Given: xyz=1

•To find: (1+x+y-¹)-¹×(1+y+z-¹)-¹×(1+z+x-¹)-¹

•Solution:

(1+x+y-¹)-¹(1+y+z-¹)-¹(1+z+x-¹)-¹

=(1+x+1/y)-¹{1/(1+y+1/z)}{1/(1+z+1/x)}

=y{(y+xy+1)}{1/(z+yz+1)/z}{1/(x+xz+1)x}

$\frac{y}{y + xy + 1} \times \frac{z}{z + yz + 1} \times \frac{x}{x + xz + 1}$

=yz/(yz+xyz+1)×xz/(xz+xyz+1)×xy/(xy+xyz+1)

=yz/(yz+2)×xz/(xz+2)×xy/(xy+2) [As,xyz=1]

=xyz/(xyz+2x)×xyz/(xyz+2y)×xyz/(xyz+2z)

=1/(1+2x)×1/(1+2y)×1/(1+2z)

$\frac{1}{1 + 2x} \times \frac{1}{1 + 2y} \times \frac{1}{1 + 2z}$

=1/(1+2x)(1+2y)(1+2z)

This will be your answer.

[Note]:There was a mistake in the question.(1+x+y-¹)-¹ should be fit here otherwise the math could not solve.