SOLUTION: Proof of 2=1
a = b
a2 = ab
a2 - b2 = ab - b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1
Can you put these statements in order and give the reasons?
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-> SOLUTION: Proof of 2=1
a = b
a2 = ab
a2 - b2 = ab - b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1
Can you put these statements in order and give the reasons?
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a = b
a2 = ab
a2 - b2 = ab - b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1
Can you put these statements in order and give the reasons? Found 2 solutions by Edwin McCravy, ikleyn:Answer by Edwin McCravy(20056) (Show Source):
a = b <--a and b can stand for the same quantity.
aČ = ab <--we can multiply both sides by a.
aČ - bČ = ab - b2 <--we can subtract bČ from both sides.
(a-b)(a+b) = b(a-b) <--we factor both sides of the equation.
a+b = b <--we divide both side by (a-b)
b+b = b <--since a = b, we can substitute b for a
2b = b <--combine like terms b+b and get 2b
2 = 1 <--we divide both sides by b
The fallacy is in the step colored red. Since a=b, (a-b)=0 and
we may never divide by 0, even when it's camouflaged as (a-b).
Edwin
You can put this solution on YOUR website! .
a = b
a2 = ab
a2 - b2 = ab - b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1
Can you put these statements in order and give the reasons?
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a = b
= - = -
(a-b)(a+b) = b(a-b) <<< You can not cancel the term (a-b), because it is zero due to a = b (see very first line). You can not divide by zero!!! Here is the key!
The rest of the proof is just not relevant. It is very old math joke.
a+b = b
b+b = b
2b = b
2 = 1
