Single correct option
If x and y are real numbers with x + y = 10, what is the minimum possible value of x² + xy + y²?
- A. 75
- B. 25
- C. 50
- D. 100
Show answer and solution
Answer: (A) 75
x² + xy + y² = (x + y)² − xy = 100 − xy.
This is minimised when xy is maximised. For a fixed sum 10, xy is maximum when x = y = 5, giving xy = 25.
Minimum = 100 − 25 = 75.
(Note xy has no lower bound, so x² + xy + y² has no maximum.)
This is minimised when xy is maximised. For a fixed sum 10, xy is maximum when x = y = 5, giving xy = 25.
Minimum = 100 − 25 = 75.
(Note xy has no lower bound, so x² + xy + y² has no maximum.)
Saved on this device. Sign in or create a free account to keep it on every device.