# Is 2 = 1?

Algebra Level 1

What is wrong with the following "proof"?

Let $$a = b=1$$, then $$a=b.$$

Step 1: $$a^2 = ab$$

Step 2: $$a^2 - b^2 = ab - b^2$$

Step 3: $$(a+b)(a-b) = b(a-b)$$

Step 4: $$a+b= \dfrac{b(a-b)}{a-b}$$

Step 5: $$a+b = b$$

Conclusion : By substituting, $$a = b = 1$$ , $$1+1 = 1 \ , \ 2 = 1$$ .

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