Question

If abc=1 then show that 1/1+a+b^-1 + 1/1+b+c^-1 + 1/1+c+a^-1 =1

Answer 1

Answer:

Step-by-step explanation:

abc=1

⟹c=1/ab

1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=1+b+ab/(1+b+ab)

=1

Answer 2

Prove by adjusting the variable a, b and c

Step-by-step explanation:

L.H.S.=

1 1 1

--------------- + --------------- + ---------------

1+ a + 1/b 1+ b + 1/c 1+ c + 1/a

b×1 1 ab

= --------------- + --------------- + ----------------

b( 1+ a + 1/b) ( 1+ b + 1/c) ab (1+ c + 1/a)

(1/c= ab)

b 1 ab

= --------------- + -------------------- + -----------------

b+ ab +1 1+ b + ab ab+ abc +b

b 1 ab

= --------------- + ----------------- + -------------

b + 1 + ab b+ 1 + ab ab+ 1 +b

b + 1+ ab

= ------------------- = 1. proved

b+1 + ab