會考數學題 - Ans.fyi 參考答案

會考數學題

用戶86933

2011-01-15 9:57 pm

平行四邊形PQRS的頂點P=(0,0) Q=(a,b) S=(-b,a) 求R
答案是(a-b , a+b) 求解釋步驟

若log x : log y = m : n 則x = ???
答案是y^(m/n) 求解釋步驟

若f(x) = x - 1/x
則f(x) - f(1/x) = ???
答案是2(x- 1/x) 求解釋步驟

若(x-2)(x-3) = (a-2)(a-3)
求x
答案是x=a 或 5-a 求解釋步驟

回答 (1)

myisland8132

2011-01-15 10:12 pm

✔ 最佳答案

1 QS的中點M為[(a - b)/2, (a + b)/2]。而此一M點亦是P和R(x,y)之中點﹐因此 x/2 = (a - b)/2 ; y = (a + b)/2 即得 R (a - b , a + b)

2 log x : log y = m : n

n log x = m log y

log x^n = log y^n

x^n = y^m

x = y^(m/n)

3 f(x) = x - 1/x; f(1/x) = 1/x - x

f(x) - f(1/x) = ( x - 1/x ) - ( 1/x - x ) = 2( x - 1/x )

4 (x - 2)(x - 3) = (a - 2)(a - 3)

x^2 - 5x + 6 = a^2 - 5a + 6

x^2 - 5x + 5a - a^2 = 0

(x - a)(x + a - 5) = 0

x = a or x = 5 - a

2011-01-15 14:14:23 補充：
Q1 y = (a + b)/2 應是 y/2 = (a + b)/2

2011-01-15 16:03:56 補充：
Trial and error only

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