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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