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, \( a = b = 1 \implies 1+1 = 1 \implies 2 = 1.\)
by
Anish Harsha