Problem Solving

billy was doing maths. He proceeded as follows,

Let, a=b

Multiplying both the sides with a, he got, a2=ab

Subtracting b2, from both the sides, he got, a2- b2= ab- b2

Now, a2- b2 = (a+b)(a-b)

So, (a+b)(a-b)= ab- b2

Taking b as common, (a+b)(a-b)=b(a-b)

Now, cancelling the common term (a-b), he got, (a+b)=b

Now the magic, as a=b (taken), if he takes a=b=1 then 1+1=1 or 2=1!

at a+b=b,
if we now proceed by equating the equation to zero, a+b-b=0 ( making the equation to zero and balance it )

a=0 , which there by translates b also =0

And there after a+b=b also holds good, with a+b=b, which is 0+0=0