Prove that a²+b²+c²-ab-bc-ca is always non negative for all values of A, B and C.
Answers
Answered by
19
a2 + b2 +c2 - ab - bc - ca
2/2(a2 + b2 +c2 - ab - bc - ca)
1/2(2a2 + 2b2 +2c2 - 2ab - 2bc - 2ca)
1/2(a2 + b2 - 2ab +b2 +c2 - 2bc + c2 + a2 - ca)
1/2[(a - b)square + (b - c)square + (c - a)square]
As squares of any real numbers can't be negative, therefore is always non negative for all values of a, b, c.
2/2(a2 + b2 +c2 - ab - bc - ca)
1/2(2a2 + 2b2 +2c2 - 2ab - 2bc - 2ca)
1/2(a2 + b2 - 2ab +b2 +c2 - 2bc + c2 + a2 - ca)
1/2[(a - b)square + (b - c)square + (c - a)square]
As squares of any real numbers can't be negative, therefore is always non negative for all values of a, b, c.
Answered by
12
Please see below
There is an attachment
Attachments:
Similar questions