Question

5.1 a
prove that a² + b ² + c² - ab-bc- ca is
values of a, b and c.
always non-negative for all​

Answer 1

Answer:

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

$2/2(a2 + b2 +c2 - ab - bc - ca)$

$1/2(2a2 + 2b2 +2c2 - 2ab - 2bc - 2ca)$

$1/2(a2 + b2 - 2ab +b2 +c2 - 2bc + c2 + a2 - ca)$

$1/2[(a - b)square + (b - c)square + (c - a)square]$

As squares of any real numbers can't be negative, therefore is always non negative for all values of a, b, c.