Question

Use the identity x^3+y^3+z^3−3xyz=(x+y+z)(x^2+y^2+z^2−xy−yz−zx) to determine the value of the sum of three integers given:


the sum of their squares is 110,

the sum of their cubes is 684,

the product of the three integers is 210,

and the sum of any two products (xy+yz+zx) is 107.

Answer 1

Inserting all the given information into the identity, we have

$684-3(210)=(x+y+z)(110-107)\implies x+y+z=18$