# Is 2=1?

Algebra Level 2

Following are some steps to prove that 2=1 :

Step 1: Let A = B

Step 2: Multiply both sides by A:- A² = AB

Step 3: Subtract B² from both sides:- A² - B² = AB - B²

Step 4: Factorize both sides:- ( A + B )( A - B ) = B ( A - B )

Step 5: Divide both sides by ( A - B ) to obtain A + B = B

Step 6: Since A = B hence B + B = B

Step 7: Simplify to obtain 2B = B

Step 8: Divide both sides by B to obtain 2=1.............hence proved.

Which step in the proof is mathematically wrong?

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