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( 條數)
The total number of pairs of integers (x,y) which satisfy the equation:
X^2-4xy+5y^2+2y-4=0 is_____________.
Ans: 8
想知點樣計呢類型ge 數
out 左c 的數學題
2010-07-05 9:10 pm
回答 (1)
2010-07-05 9:21 pm
✔ 最佳答案
X^2-4xy+5y^2+2y-4=0(x^2 - 4xy + 4y^2) + y^2 + 2y - 4 = 0
(x - 2y)^2 + (y^2 + 2y + 1) - 5 = 0
(x - 2y)^2 + (y + 1)^2 = 5
Let M = x - 2y , N = y + 1 ,
M^2 + N^2 = 5
M = +/-1 , N = +/- 2
2 x 2 = 4 pairs of (x,y)
or
M = +/-2 , N = +/-1
2 x 2 = 4 pairs of (x,y)
Total = 4 + 4 = 8 pairs of (x,y)
收錄日期: 2021-04-21 22:15:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100705000051KK00502