Answer:
Given:- xyz=1
To prove:- (1+x+y
−1
)
+(1+y+z
+(1+z+x
=1
Proof:-
Taking L.H.S.-
(1+x+y
=(1+x+xz)
+(1+y+xy)
+(1+z+yz)
+(xyz+y+xy)
+y
(1+x+xz)
(1+y
)+(1+z+yz)
=(xyz+x+xz)
=x
(1+z+yz)
=(1+z+yz)
(x
+(xy)
(yz+z+1)
=
1+z+yz
= R.H.S.
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Answers & Comments
Answer:
Given:- xyz=1
To prove:- (1+x+y
−1
)
−1
+(1+y+z
−1
)
−1
+(1+z+x
−1
)
−1
=1
Proof:-
Taking L.H.S.-
(1+x+y
−1
)
−1
+(1+y+z
−1
)
−1
+(1+z+x
−1
)
−1
=(1+x+xz)
−1
+(1+y+xy)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
+(xyz+y+xy)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
+y
−1
(1+x+xz)
−1
+(1+z+yz)
−1
=(1+x+xz)
−1
(1+y
−1
)+(1+z+yz)
−1
=(xyz+x+xz)
−1
(1+y
−1
)+(1+z+yz)
−1
=x
−1
(1+z+yz)
−1
(1+y
−1
)+(1+z+yz)
−1
=(1+z+yz)
−1
(x
−1
+(xy)
−1
)+(1+z+yz)
−1
=(1+z+yz)
−1
(yz+z+1)
=
1+z+yz
1+z+yz
=1
= R.H.S.