If x + y + z = 0, show that x³ + y³ + z³ = 3xyz.

Solution:

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

If x + y + z = 0, then the entire RHS becomes 0.

Hence the LHS x³ + y³ + z³ - 3xyz = 0

Thus, x³ + y³ + z³ = 3xyz

☛ Check: NCERT Solutions for Class 9 Maths Chapter 2

Video Solution:

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz.

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 13

Summary:

Thus, we see that if x + y + z = 0, then x³ + y³ + z³ = 3xyz

☛ Related Questions:

• Verify:i) (x³ + y³) = (x + y)(x² - xy + y²)ii) (x³ - y³) = (x - y)(x² + xy + y²)
• Factorise each of the following:i) 27y³ + 125z³ii) 64m³ - 343n³ = (4m)³ - (7n)³[Hint: See Question 9.]
• Factorise: 27x³ + y³ + z³ - 9xyz
• Verify that x³ + y³ + z³ - 3xy = 1/2 (x + y + z)[(x - y)² + (y - z)² + (z - x)²]