f4 math - Ans.fyi 參考答案

f4 math

[匿名]

2014-03-20 11:55 am

1)3^(x+1)-2^(y+1)=1
4(3^x)+3(2^y)=24
求x

2)log_5 15 =r
以r表示log_3 5

3)O, A, B(16, 8), C 是菱形的頂點, 其中O為原點, A則是x軸上的一點
求A 和C的座標

更新1:

問多條 y=x+ 2/x , 以y表示x^2+ 4/x^2 thanks

更新2:

圓與y軸相切, 並通過A(1, -1), 圓心C位於直線L : x+y=7上求圓可能的方程

回答 (1)

用戶10012

2014-03-20 3:37 pm

✔ 最佳答案

(1) Let 3^x = u and 2^y = v
so 3u - 2v = 1 ..........(1)
4u + 3v = 24 ..........(2)
(1) x 3 + (2) x 2
9u - 6v + 8u + 6v = 3 + 48
17u = 51
so u = 3 = 3^x, so x = 1.
(2)
log 15/log 5 = r = log (3x 5)/log 5 = ( log 3 + log 5)/log 5 = log 3/log 5 + 1
so log3/log5 = r - 1
log 5/log 3 = 1/(r - 1).
(3) Assume OABC is in anti- clockwise order.
Let A be ( a, 0)
(i) For rhombus, OA = AB
a^2 = (16 - a)^2 + (8 - 0)^2
a^2 = 256 - 32a + a^2 + 64
a = (256 + 64)/32 = 10, so A is (10,0)
Since OABC is a parallelogram, when A shifts to B, O shifts to C,
so C is ( 16 - 10, 8 - 0) = (6, 8).

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