How to make (1 = 2) in math?

Asked on by loraaa

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embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

There are multiple versions of this; the key is to try to find what is wrong with the "proof": Let a=b; then

`a=b` Given

`a^2=ab` Multiply both sides by a

`a^2+a^2=a^2+ab` Add `a^2` to both sides

`2a^2=a^2+ab` Collect like terms

`2a^2-2ab=a^2+ab-2ab` Subtract 2ab from both sides

`2a^2-2ab=a^2-ab` Collect like terms

`2(a^2-ab)=1(a^2-ab)` Distributive property

`2=1` Divide both sides by `a^2-ab`

Thus 1=2.

najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

Problem with the above solution is that you are dividing both sides with (a^2 - ab) which is zero because a=b (assumed).

Any quantity divided by zero is an indeterminate

You cannot divide by zero and that is what's wrong with the proof.

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