What is the minimum value of X + y + Z = 1, √ (x * 2 + XY + y * 2) + √ (Z * 2 + ZY + y * 2) + √ (x * 2 + XZ + Z * 2)?

4 (XX + XY + YY) - 3 (x + y) ^ 2 = (X-Y) ^ 2 > = 0 can be obtained: √ (x ^ 2 + XY + y ^ 2) > = √ 3 / 2 (x + y) similarly: √ (y ^ 2 + ZY + Z ^ 2) > = √ 3 / 2 (y + Z) √ (Z ^ 2 + XZ + x ^ 2) > = √ 3 / 2 (x + Z) add: √ (x ^ 2 + XY + y ^ 2) + √ (y ^ 2 + YZ + Z ^ 2) + √ (Z ^ 2 + ZX ^ 2) > = (√ 3 / 2) * (x + y +

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