Question

Prove that 2a2 +2b2 +2c2 -2ab-2bc-2ca = (a-b)2 +(b-c)2 +(c-a)2

Answer 1

Step-by-step explanation:

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Answer 2

(a-b)2 = a2-2ab+b2 .................. (1)

(b-c)2 = b2-2bc+c2 .................. (2)

(c-a)2 = c2-2ca+a2 ..................(3)

therefor,

2a2+2b2+2c2-2ab-2bc-2ca

=(a2-2ab+b2)+(b2-2bc+c2)+(c2-2ca+a2)

=(a-b)2+(b-c)2+(c-a)2 (from 1,2and 3)

(proved)