Question

If abc = 1, prove that E (1 + a + b-1)-1​

Answer 1

Given,

E (1 + a + b-1)-1

• Add 1 to 1st term on LHS, add 1 to second term and again 1 to last term. Balance this by adding 3 to the RHS.

[(a/1-a) + 1 ] + [(b/1-b) + 1 ] + [ (c/1-c) + 1] = 1 + 3

• Perform the operations within the three square brackets on LHS and get,

(a + 1 - a)/(1-a) + (b+1-b)/(1-b) + (c + 1-c)/ (1-c) = 4

Simplifying the quantities within round brackets on LHS, we obtain

• (1/1-a) + (1/1-b) + (1/1-c) = 4 (Q.E.D.)