006ruler Posted:

Step 1: Let a=b.

Step 2: Then , a^2 = ab

Step 3: a^2+a^2 = a^2 + ab ,

Step 4: 2a^2 = a^2 + ab,

Step 5: 2a^2 – 2ab = a^2 + ab – 2ab,

Step 6: and 2a^2 – 2ab = a^2 – ab.

Step 7: This can be written as 2(a^2 – ab) = a^2 – ab,

Step 8: and cancelling the (a^2 – ab) from both sides gives 1=2.

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Misunderstanding #1: You divided by zero when you cancelled in step 8. As it said at the top, a^2 and ab are equal, so a^2 – ab = 0. What you had on line 7 was equivalent to 2*0 = 0, which is true, but it’s not valid to “cancel” the zero to get 2=1