Learn If X Y Z 0 Show That X3 Y3 Z3 3xyz

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# 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

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