If x, y are integral solutions of 2x 2 – 3xy – 2y 2 = 7, then find the value of |x + y|
Text Solution
Verified by Experts4
(4)
Sol. 2x 2 – 4xy + xy – 2y 2 = 7
2x (x – 2y) + y(x – 2y) = 7
(x – 2y) (2x + y) = 7
x, y are integers ⇒ x – 2y, 2x + y are also integers
Four cases are possible
Case I x – 2y = 1, 2x + y = 7 ⇒ x = 3, y = 1
|x + y| = 4
Case II x – 2y = 7, 2x + y = 1 ⇒ x = 
rejected
Case III x – 2y = –1, 2x + y = –7
⇒ x = –3, y = –1
|x + y| = 4
Case IV x – 2y = –7, 2x + y = –1 ⇒ x = – 
rejected
Hence |x + y| = 4
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems