CT 22: Identities – IV

1. If a + b + c = 5 and a² + b² + c² = 15, then find the value of a³ + b³ + c³ - 3abc - 27. 

2. If (a + b + c) = 19 and (a² + b² + c²) = 155, find the value of (a - b)² + (b - c)² + (c - a)².

3. If (a + b + c) = 14, and (a³ + b³ + c³ - 3abc) = 98, find the value of (a² + b² + c²).

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

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

6. If (p - q) = - 6, (q - r) = 5 and (r - p) = 1, then find the value of (p³ + q³ + r³ - 3pqr)/(p + q + r).

7. If x4+1 /x4=47, then what is the value of x3+1 /x3?

8. If x² + y² + z² - 2x + 4y - 2z + 6 = 0, what is the value of 2x - 3y + z?

9. If a² + b² + c² + 2a + 4b + 6c = -14 then 

(a + b + c)/(b + c) = ?

10. If x³ + 1/x³  = 2, then find the value of x² - 2x.