CT 19: Identities – I

1. The value of x² + y² when x = 1, y = 2 is:

2. If a = 101, b = 102 and c = 103, then a² + b² + c² − ab − bc − ca = _______.

3. If a² + b² + c² - ab - bc - ca = 0 then

4. What is the value of a² + b² + c², if a + b + c = 9 and ab + bc + ca = 23?

5. If x + y = 7 and xy = 19, then calculate the value of x² + y².

6. What is the value of (a² + b² + 4c² - ab - 2bc - 2ca)(a + b +2c)?

7. If 4x² + y² = 40 and xy = 6, find the positive value of 2x + y.

8.  If x⁴ + x² y² + y⁴ = 128 and x² + y² + xy = 16, find the value of x² + y² - xy.

9. What is the value of a² + 4b² + 9c² - 4ab + 12bc - 6ca? 

10. If