Question

Solve for (x, y, z) if x + y + z = 3, x2 + y2 + z2 = 3, x3 + y3 + z3 = 3

Answer 1

(x+y+z)²=(3)²

x²+y²+z²+2xy+2yz+2zx=9

3+2(xy+yz+zx)=9

2(xy+yz+zx)=9-3

xy+yz+zx =6

x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)

3-3xyz=(3)(3-(xy+yz+zx)

3-3xyz=(3)(3-(6)

3-3xyz=3×-3

3-3xyz=-9

-3xyz= -9-3

-3xyz= -12

xyz= -12/-3

xyz= 4

I Hope it's help you