Question

If a^2=2 then prove that a+1=a-1/3-2a

Answer 1

a+1=(a-1)/3-2a. (a+1)(3-2a)=a-1. 3a-2a²+3-2a=a-1. 3a-2a-a-2a²=-1-3. -2a²=-4. -2×2=-4. -4=-4. Lhs =Rhs. Hence proved.

Answer 2

We have a²=2
         ⇒ a²-1= 2-1
         ⇒ (a+1)(a-1) = 1
         ⇒ (a+1) =1/(a-1)
RHS= (a-1)/(3-2a)
       = (a-1)/(2+1-2a)
       = (a-1)/ (a²+1-2a)       as  a²=2
       = (a-1)/(a-1)²
       = 1/(a-1)
       = a+1= LHS