If x + y + z = 25, $x^3 + y^3 + z^3 = 85$ and xyz = 20, then find the value of $x^2 + y^2 + z^2 - xy - yz - zx $.

1 

x + y + z = 25

x³ + y³ + z³ = 85

xyz = 20

We know that,

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

= 85 - 3(20) = (25)( x² + y² + z² - xy - yz - zx)

= (x² + y² + z²  - xy - yz - zx)(25) = 85 - 60 = 25

= x² + y² + z² - xy - yz - zx = 1