If x - y = 1 and x2 + y2 = 41 where x,y ≥ 0, then the value of x + y will be :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 9.
Concept used:
(x - y)2 = x2 + y2 - 2xy ---- (1)
(x + y)2 = x2 + y2 + 2xy
Calculations:
⇒ x - y = 1 and x2 + y2 = 41
Using equation (1), we get
⇒ 1 = 41 - 2xy
⇒ 2xy = 40
⇒ xy = 20
Using equation (2)
⇒ (x + y)2 = 41 + 40
⇒ (x + y)2 = 81
⇒ (x + y) = 9