CT 28: Identities – IV

1.If x + y + z = 0 then x³ + y³ + z³ + 3xyz is equal to

2. If x - y + z = 0, then find the value of  (y²/2xz) - (x²/2yz) - (z²/2xy)

3. If a + b + c = 0, then the value of (a + b - c)² + (b + c - a)² + (c + a - b)² is

4. If x + y + z = 0, then what will be the value of ?

5. If a + b - c = 0, then what is the value of ?

6. Select the value that will come in place of '?' in the following expression.

If a + b + c = 0, then a³+ b³ + c³ = ? × abc

7. If a + b + c = 0, then what is the value of ?

8. If a + b + c = 0, then is equal to:

9. If x + y + z = 0, then (x + y - z)³ + (y + z - x)³ + (z + x - y)³ = k(xyz), where k is equal to:

10. If a + b + c = 0 then find the value of (a² + b² + c²)/(ab + bc + ca).