Question

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

• A. 3
• B. 5
• C. 6
• D. 4

Answer 1

Answer:

A. 3

Solution:

Given:

x + y + z = 10, (x³ + y³ + z³) = 75 and xyz = 15

Formula:

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

Calculation:

According to the given formula

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

⇒ 75 - 3 $\times$ 15 = 10 $\times$ (x² + y² + z² - xy - yz - zx)

⇒ 75 - 45 = 10 $\times$ (x² + y² + z² - xy - yz - zx)

⇒ (x² + y² + z² - xy - yz - zx) = $\frac{30}{10}$ 

∴ x² + y² + z² - xy - yz - zx = 3

Hence option(A) is correct answer.