Question

verify a²+b²+c²-ab-bc-ca=1/2((a-b)²+(b-c)²+(c-a)²)​

Answer 1

Answer:

RHS = 1/2 (a-b) ^2 + ( b-c) ^2 + (c-a) ^2

= 1/2( a^2 +b^2 - 2ab + b^2 + c^2 -2bc + c^2 + a^2 - 2ac)

= 1/2( a^2 + a^2 + b^2 + b^2 + c^2 + c^2 - 2ab -2bc - 2ca)

= 1/2[1/2( a^2+ b^2+ c^2 -ab -bc -ca) ]

= a^2 + b^2 + c^2 - ab - bc - ca