Yefim S. answered 06/09/23
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y = 9 - x; Q = 6x2 + 3(9 - x)2; Q = 9x2 - 54 x + 243; Q' = 18x - 54 = 0; x = 3; y = 9 - 3 = 6. Q'' = 18 > 0, minimum
Qmin = Q(3, 6) = 54 + 108 = 162