An ice chest contains 2 bottles of orange juice, 5 bottles of grape juice, and 1 bottle of apple juice, all buried in ice. What’
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the sum of their squares is 110, So
the sum of their cubes is 684, so
the product of the three integers is 210, so xyz= 210
the sum of any two products (xy+yz+zx) is 107
Now we plug in all the values in the identity
684 - 3(210) = (x+y+z)(110-107)
684 - 630 = (x+y+z)(3)
54 = 3(x+y+z)
Divide by 3 on both sides
18 = x+y+z
the value of the sum of three integers is 18