If x + y + z = 10, $x^3 + y^3 + z^3 = 75$ and xyz = 15, then find the value of $x^2 + y^2 + z^2 - xy - yz - zx$
Answer & explanation
Correct answer: option 2
x + y + z = 10,
(x3 + y3 + z3) = 75
xyz = 15
We know that,
(x3 + y3 + z3 - 3xyz) = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
According to the formula
= 75 - 3 × 15 = 10 × (x2 + y2 + z2 - xy - yz - zx)
= 75 - 45 = 10 × (x2 + y2 + z2 - xy - yz - zx)
= (x2 + y2 + z2 - xy - yz - zx)= \(\frac{30}{10}\)
(x2 + y2 + z2 - xy - yz - zx)= 3