Sum and Square Sum

Algebra Level 5

(x,y,z)R3 (x, y, z) \in \mathbb{R}^3 are points that lie on the plane x+2y+3z=78 x + 2y + 3z = 78, and lie on the sphere x2+y2+z2=468x^2 + y^2 + z^2 = 468. The maximum value of xx has the form ab \frac {a}{b} , where aa and bb are coprime positive integers. What is the value of a+b a+b?

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