If x + y + z = 10, $x^3 + y^3 + z^3 = 75$ and xyz = 15, then find the value of $x^2 + y^2 + z^2 - xy - yz - zx$

3

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