Pairwise Products

Algebra Level 2

xy=24xz=30yz=15\large xy = 24 \quad xz = 30 \quad yz = 15

If x,y,zx,y,z are positive, then x+y+zx + y + z can be written as abc\frac{a\sqrt{b}}{c}, where a,ba,b and cc are positive integers, with aa and cc are relatively prime, and bb is square-free. Find a+b+ca+b+c.

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