### 2 . Fallacy

Let **a ≠ b **and **c** is the **arithmetic mean** of **a** and** b** .

Then ,

**a + b = 2c **

**Multiplying** in both side by **( a- b)**

(a + b)**( a- b)** = 2c **( a- b)**

a^{2} – b^{2 }= 2ac – 2bc

a^{2} – 2ac = b^{2 }– 2bc

**Add** in both side **c**^{2}.

a^{2} – 2ac **+ c**^{2} = b^{2 }– 2bc **+ c**^{2 }.

**( a -c )**^{2} = ( b – c )^{2 }

**a – c = b – c**

here **c** is **cancel** out in both** side**

**a = b **but as initially **a ≠ b**

Which is **impossible**.