Given 14 (XX + YY + zz) = (x + 2Y + 3Z) ^ 2, find X: Y: Z

10: Y: z = 1:2:3 because: 14 (XX + YY + zz) = (x + 2Y + 3Z) ^ 214 (XX + YY + zz) - (x + 2Y + 3Z) ^ 2 = 013x ^ 2 + 10Y ^ 2 + 5Z ^ 2-4xy-6xz-12yz = 0 (4x ^ 2-4xy + y ^ 2) + (9x ^ 2-6xz + Z ^ 2) + (9y ^ 2-12yz + 4Z ^ 2) = 0 (2x-y) ^ 2 + (3x-z) ^ 2 + (3y-2z) ^ 2 = 0, so 2x-y = 0, 3x-z = 0, 3y-2z = 0

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