Question

if xyz=1 show that 1/1+x+y^-1 + 1/1+y+z^-1 + 1/1+z+x^-1 = 1​

Answer 1

Step-by-step explanation:

Given:— xyz = 1

To prove:- = 1/1+x+y^-1 + 1/1+y+z^-1 + 1/1+z+x^-1 = 1

Proof:-

Taking L.H.S.-

= 1/1+x+y^-1 + 1/1+y+z^-1 + 1/1+z+x^-1

= 1/1+x+1/y + 1/1+y+1/z + 1/1+z+1/z

= y/y+xy+1 + 1/1+y+xy + 1/1+1/xy+1/x

[∵ xyz = 1 => z = 1/xy and 1/z = xy]

= y/y+xy+1 + 1/1+y+xy + xy/xy+1+y

= y+1+xy /xy+y+1

= 1.

= R.H.S

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