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Suppose the average of 5 5 5 positive numbers is equal to 2. 2. 2. What is the maximum possible product of the numbers?
Suppose xyz=8 xyz = 8 xyz=8 with x,y,z>0.x, y, z > 0. x,y,z>0. What is the minimum value of x+y+z x + y + z x+y+z?
What is the largest n n n for which
x3+y3+z3≥nxyz x^3 + y^3 + z^3 \geq nxyz x3+y3+z3≥nxyz
holds for all x,y,z>0 x, y, z > 0 x,y,z>0?
(x+y)(y+z)(x+z)≥nxyz (x + y)(y + z)(x + z) \geq nxyz (x+y)(y+z)(x+z)≥nxyz
holds for all positive x,y,z x, y, z x,y,z?
Suppose 2x+3y+z=18. 2x + 3y + z = 18. 2x+3y+z=18. Find the maximum value of xyz xyz xyz for x,y,z>0. x, y, z > 0. x,y,z>0.
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