CT 29: Identities – V

1.If a + b + c = 0 and a² + b² + c² = 40, then what is the value of 4ab + 4bc + 4ca?

2. If  then what is the value x³ - y³ ?

3. If x = b + c, y = c + a, z = a + b, then what is (x + y + z)³ – 24xyz equal to ?

4. If (a + b + c)/2 = 16 and 2ab + 2bc + 2ca = 120, then what is the value of 4a² + 4b² + 4c²?

5. If a, b, c, x, y, z are real numbers such that (a + b + c)² - 3(ab + bc + ca) + 3(x² + y² + z²) = 0, then which one of the following is correct?

6. Find the value of p¹¹¹⁹ - 1154p¹¹¹¹ + p¹¹⁰³ if (p+1/p)  = 2√2.

7. If a^1/3+b^1/3+c^1/3=0, then (a + b + c)³ :

8. If x + y + z = 3 and x² + y² + z² = 101, then what is the value of 

9. If (a+1/a)² = 3, find the value of a²¹⁸ + a²¹² + a²⁴ + a¹⁸

10. If x + y + z = 0, then find the value of .