Question

已知x+y+z=3,X的平方+y的平方+z的平方=29,x的立方+y的立方+z的立方=45,求xyz的值

Answer 1

X+Y+Z=3

X^3+Y^3+Z^3+6XYZ+3X^2Y+3XY^2+3Y^2Z+3YZ^2+3Z^2X+3ZX^2=3^3=27

X^3+Y^3+Z^3=45

6XYZ+3X^2Y+3XY^2+3Y^2Z+3YZ^2+3Z^2X+3ZX^2=-18

X^2+Y^2+Z^2=29

X^3+Y^3+Z^3+X^2Y+XY^2+Y^2Z+YZ^2+Z^2X+ZX^2=3*9=87

X^2Y+XY^2+Y^2Z+YZ^2+Z^2X+ZX^2=42

XYZ=-24