Maximizing in a Real Quadratic

Algebra Level 5

a,b a, b and cc are real values satisfying a+2b+3c=195 a + 2b + 3c = 195 and a2+b2+c2=2925a^2 + b^2 + c^2 = 2925 . The maximum value of aa has the form pq \frac {p}{q} , where pp and qq are positive, coprime integers. What is the value of p+q p + q?

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