用代數方法解這聯立方程
x²-y²=3x+y=7
數 學 問 題
2013-09-29 3:14 am
回答 (4)
2013-09-29 7:58 pm
✔ 最佳答案
x^2 - y^2 = 3x + y = 7y = 7 - 3xSo, x^2 - (7 - 3x)^2 = 7x^2 - 49 + 42x - 9x^2 = 74x^2 - 21x + 28 = 0x = (21±7√i)/8當x = (21 - 7√i)/8, y = (-7 + 3√7i)/8當x = (21 + 7√i)/8, y = (-7 - 3√7i)/8
2013-09-29 5:10 pm
題目應該是：
x² - y² = 3...(1)
x + y = 7.....(2)
(2) 得 y = 7 - x 代入 (1)
x² - (7 - x)² = 3
==> 14x - 49 = 3
==> x = 26/7
代入 (2), 得 y = 7 - 26/7 = 23/7
答案：x = 26/7, y=23/7
x² - y² = 3...(1)
x + y = 7.....(2)
(2) 得 y = 7 - x 代入 (1)
x² - (7 - x)² = 3
==> 14x - 49 = 3
==> x = 26/7
代入 (2), 得 y = 7 - 26/7 = 23/7
答案：x = 26/7, y=23/7
2013-09-29 5:52 am
先注意小心題目的寫法和理解：
x²-y²=3x+y=7
即是
{x²-y²=7...(1)
{3x+y=7...(2)
(2)得 y = 7-3x 代入(1)
x² - (7-3x)² = 7
x² - (49-42x+9x²) = 7
x² - 49+42x-9x² = 7
8x²-42x+56=0
4x²-21x+28=0
x = [21±√(7)i]/8
y = 7-3x
所以，(x,y) = ( [21+√(7)i]/8, [-7-3√(7)i]/8 ) or ( [21-√(7)i]/8, [-7+3√(7)i]/8 )
x²-y²=3x+y=7
即是
{x²-y²=7...(1)
{3x+y=7...(2)
(2)得 y = 7-3x 代入(1)
x² - (7-3x)² = 7
x² - (49-42x+9x²) = 7
x² - 49+42x-9x² = 7
8x²-42x+56=0
4x²-21x+28=0
x = [21±√(7)i]/8
y = 7-3x
所以，(x,y) = ( [21+√(7)i]/8, [-7-3√(7)i]/8 ) or ( [21-√(7)i]/8, [-7+3√(7)i]/8 )
2013-09-29 3:27 am
x²-y²=3
x+y=7
x = 7 - y
(7-y)² - y² = 0
49-14y+y² -y² = 0
49-14y = 0
49 = 14y
y = 49/14 = 7/2
x+y=7
x = 7 - y
(7-y)² - y² = 0
49-14y+y² -y² = 0
49-14y = 0
49 = 14y
y = 49/14 = 7/2
收錄日期: 2021-04-13 19:43:51
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130928000051KK00185