數 學 問 題

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

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

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=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