Question 7
If $$ 3 ( a^2 + b^2 + c^2) = ( a + b + c)^2 $$, then the relation between a,b and c is
Solution
solution
$$ 3 ( a^2 + b^2 + c^2) = ( a + b + c)^2 $$
we know
$$( a + b + c)^2 = a^2 + b^2 + c^2 +2(ab +bc +ca)$$
$$3 ( a^2 + b^2 + c^2) = a^2 + b^2 + c^2 +2(ab +bc +ca)$$
$$2 ( a^2 + b^2 + c^2) = 2(ab +bc +ca)$$
$$ ( a^2 + b^2 + c^2) = (ab +bc +ca)$$
as we can observe the symmetry
$$a= b = c$$
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