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 $.
Answer & explanation
Correct answer: option 2
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