SOLUTION: if a=b then a*a=a*b a^2=ab a^2-b^2=ab-b^2 (a+b)(a-b)=b(a-b) a+b=b a+a=a 2a=a it contradicts the assumption.. what is wrong in this ?

Algebra ->  College  -> Linear Algebra -> SOLUTION: if a=b then a*a=a*b a^2=ab a^2-b^2=ab-b^2 (a+b)(a-b)=b(a-b) a+b=b a+a=a 2a=a it contradicts the assumption.. what is wrong in this ?      Log On


   

Question 25717: if a=b
then
a*a=a*b
a^2=ab
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
a+b=b
a+a=a
2a=a
it contradicts the assumption..
what is wrong in this ?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
When you had (a+b)(a-b)=b(a-b) you divided both sides
by (a-b) to get a+b=b.
But in doing that you divided by zero because you
started the argument by saying a=b.
Dividing by zero is an illegal move, i.e. it is
meaningless; so you ended up with a meaningless
conclusion.
Cheers,
Stan H.