Question

Please give this answer!​

Answer 1

Step-by-step explanation:

Question:- If abc = 1, show that 1/1+a+b⁻¹ + 1/1+b+c⁻¹ + 1/1+c+a⁻¹ = 1

Sol:- 1/1+a+b⁻¹ + 1/1+b+c⁻¹ + 1/1+c+a⁻¹ =1

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

= b/ b+ab+1 + c/ c+bc+1 + a/ a+ac+1 __(1)

It is given that, abc = 1

So, c = 1/ab

By putting the value of c in equation (1).

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

= b/ b+ab+1 + 1/ab×ab/ 1+b+ab + ab/ 1+ab+b

= b/ b+ab+1 + 1/ 1+b+ab + ab/ 1+ab+b

= 1+ab+b/ b+ab+1

= 1