✔ 最佳答案
(1) √(x/y) + √(y/x) = 5/2
(x + y)/√(xy) = 5/2
√(xy) = (10)(2/5) = 4
xy = 16
y = 16/x
x + y = 10 => 16/x + x = 10
x^2 - 10x + 16 = 0
(x - 2)(x - 8) = 0
x = 2 => y = 8
x = 8 => y = 2
x,y分別是2和8
(2) (2^x)[4^(x^2+1)] = 8^(x+2)
(2^x)[2^(2x^2+2)] = 2^(3x+6)
2^(x + 2x^2 + 2) = 2^(3x+6)
x + 2x^2 + 2 = 3x + 6
2x^2 - 2x - 4 = 0
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2或x = -1
(3) 題目有誤???
(4) 二根之和 = -4 + 1 = -3 = -b/a => b = 3a
二根之積 = (-4)(1) = -4 = c/a => c = -4a
a:b:c = 1 : 3 : -4
(5) 2mx^2 - (3m+2)x + (m+1) = 0
(2x - 1)(mx - m - 1) = 0
二根為 1/2 及 1 + 1/m
(1) 1/2 + 1 + 1/m = 2 => m = 2
(2) 1 + 1/m = 0 => m = -1
(3) 1 + 1/m = 2 => m = 1
(4) 1 + 1/m = -1/2 => -2/3
(5) 1 + 1/m = -1 => m = -1/2
(6) 1 + 1/m - 1/2 = 2 => m = 2/3
2009-11-20 21:16:39 補充：
3.方程式ax^2 +bx +c =0，a不等於0，若c等於0，兩根如何？
ax^2 + bx = 0
x(ax + b) = 0
x = 0 或x = -b/a
兩根為0及-b/a
