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 ?

SOLUTION: if a=b then aa=ab 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 ?

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) (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.
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