Question 1178360
x+y+z=23

xyz=113+(x-1)(y-1)(z-1)

xyz = 113 +( xy-x-y+1)(z-1)

xyz= 113+ xyz-xy-xz+x-yz+y+z-1    (xyz) cancels off

xy+yz+zx =113+22

xy+yz+zx = 135
2(xy+yz+zx) =270

x^2+y^2+z^2=(x+y+z)^2-2(xy+yz+zx)

= 23^2-270 -259

the sum of the squares of their ages =259