Question

if x+y+z=10 and x2+y2+z2=40 find xy+yz+zx and x3+y3+z3-3xyz​

Answer 1

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

100 = 40 + 2 (xy+yz+zx)

xy + yz + zx = 30

x^3 + y^3 + z^3 - 3xyz = (x+y+z) (x^2 + y^2 + z^2 - xy - yz - zx) = 10 (40-30) = 100