查看完整版本 : Done thx

§黑紫● 2018-11-1 02:22 AM

Done thx

Done thank you.

[[i] 本帖最後由 §黑紫● 於 2018-11-5 01:35 AM 編輯 [/i]]

§黑紫● 2018-11-2 12:01 AM

Push

ppresent 2018-11-2 10:10 PM

.1a. 睇上去我估你個n-1同2n-1成個都係次方,咁加番個括號會容易啲睇
(3^2n - 9^(n-1)) / (3^(2n-1) + 3^2n)
=(3^2n - 3^(2n-2)) / (3^(2n-1) + 3^2n)
=(3^2n)(1-3^-2)/(3^2n)(3^-1+1)
=(1-1/9)/(1/3+1)
=(8/9)/(4/3)
=2/3

1b.解 3^(2x+1) - 9^x + 3^(2x-1) = 63
可以把9^x 變成 3^2x 然後你會見到3^2x係一個 common factor可以抽出黎

1c.
解 聯立方程
{3^x-2y=81
{2^2x+y=1/128

這個x-2y 是整個是次方是吧? 即是 3^(x-2y) = 81 ?
如果是這樣的話就變成 x-2y = 4 
下式同樣處理,之後得到兩條linear equations照普通方法做即可

1d.化簡(8x^2/y^4)^3/2 · (開方2y^2/x^4)
=12 x^3 / y^6 · (開方2y^2/x^4)

sqrt(2y^2/x^4) = sqrt(2)y/x^2

2a.解6^x-2= 1/開方216
1/sqrt(216) = 1/sqrt(6^3) = 1/6^(3/2) = 6^(-3/2)
不過想確定一下你個開方216會唔會係開方3次?


2b.(a-b)^2 = a^2+b^2-2ab

2c. (開方125)·[(開方60) -1] / 開方72
sqrt(125)=5sqrt(5)
sqrt(60) = 2sqrt(15)
sqrt(72) = 6sqrt(2)

2d.FD (16)轉二進數=253(10)

253= 2(126)+1
126= 2(63)+0
63 = 2(31)+1
31 = 2(15)+1
15 = 2(7) +1
7  = 2(3) +1
3 = 2(1) + 1
1 = 2(0) + 1

所以253(10進) = 11111101(2進)
另外 255(10進) = 11111111(2進) 所以亦可 減去 10(2進) 得出上面答案

二進數-11111100,如何直接轉做16進數較快?
11111100 = 11111111 - 00000011
       = 255(10進) - 3(10進)
       = 252
       = 16(15)+12
       = FC(16進)

3.解
{5^x-3·4^y=1
{2·5^x=7·4^y-6

這是3·(4^y) 還是 (3·4)^y?

[[i] 本帖最後由 ppresent 於 2018-11-2 10:11 PM 編輯 [/i]]

§黑紫● 2018-11-3 01:49 AM

1b.解 3^(2x+1) - 9^x + 3^(2x-1) = 63

* 變左3^6x=63?

1c.
解 聯立方程
{3^x-2y=81
{2^2x+y=1/128

這個x-2y 是整個是次方是吧? 即是 3^(x-2y) = 81 ?
如果是這樣的話就變成 x-2y = 4 

*唔明點會變會變成x-2y=4

2a.解6^x-2= 1/開方216
1/sqrt(216) = 1/sqrt(6^3) = 1/6^(3/2) = 6^(-3/2)
不過想確定一下你個開方216會唔會係開方3次?

*只係一個開方216的


2b.(a-b)^2 = a^2+b^2-2ab

2c. (開方125)·[(開方60) -1] / 開方72

(5sqrt(5)-2sqrt(15)-1) / 6sqrt(2)

*下一step係點做呢?

3.解
{5^x-3·4^y=1
{2·5^x=7·4^y-6

這是3·(4^y) 還是 (3·4)^y?

*是 3·(4^y)

4.想再問10+4x100+7x9

10進= 974 是嗎?

但要再計16進 同2進數
應該計邊個先較好?

把974÷2/16計出嚟唔知抄邊d數字做答案

many thanks

ppresent 2018-11-3 09:57 AM

1b.解 3^(2x+1) - 9^x + 3^(2x-1) = 63

[color=#ff8c00]3^(2x+1) -9^x + 3^(2x-1) = 63
3^(2x+1) -3^2x + 3^(2x-1) = 63
3^(2x) (3-1+1/3) = 63[/color]
[color=#ff8c00]3^(2x) (7/3) = 63[/color]

1c. *唔明點會變會變成x-2y=4
[color=#ff8c00]3^(x-2y)=81
3^(x-2y)=3^4
x-2y = 4[/color]

2c. [color=#ff8c00](5sqrt(5))(2sqrt(15)-1) / 6sqrt(2)
=(10sqrt(75)-5sqrt(5))/6sqrt(2)
=(50sqrt(3)-5sqrt(5))/6sqrt(2)
=(50sqrt(3)-5sqrt(5))sqrt(2)/12
=(50sqrt(6)-5sqrt(10))/12[/color]

3.解
{5^x-3·(4^y)=1
{2·(5^x)=7·(4^y)-6
[color=#808000]從一式可得2(5^x)-6(4^y)=2
二式可寫成2(5^x)-7(4^y)=-6
上式減去下式得出 4^y=8,
即2^(2y)=8[/color]


4.想再問10+4x100+7x9

10進= 974 是嗎?
[color=#ff8c00]這個看不太懂, 10 + 400 + 63 ?[/color]

但要再計16進 同2進數
應該計邊個先較好?

把974÷2/16計出嚟唔知抄邊d數字做答案

§黑紫● 2018-11-4 01:00 AM

[quote]原帖由 [i]ppresent[/i] 於 2018-11-3 09:57 AM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=489948527&ptid=27820074][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
1b.解 3^(2x+1) - 9^x + 3^(2x-1) = 63

3^(2x+1) -9^x + 3^(2x-1) = 63
3^(2x+1) -3^2x + 3^(2x-1) = 63
3^(2x) (3-1+1/3) = 63
3^(2x) (7/3) = 63

1c. *唔明點會變會變成x-2y=4
3^(x-2y)=81
3^(x-2y)=3^4
x-2y  ... [/quote]


題目4係 9×100+7×10+4

有勞

ppresent 2018-11-4 04:28 PM

[color=#ff8c00]974 = 16(60)+14 (14在16進制是E)[/color]
[color=#ff8c00]60= 16(3)+12 (12在16進制是C)[/color]
[color=#ff8c00]974(10進) = 3CE(16進)[/color]
[color=#ff8c00][/color]
[color=#ff8c00][/color][color=#ff8c00]Checking:[/color]
[color=#ff8c00]3*16^2+12*16+14[/color]
[color=#ff8c00]=3(256) + 192 + 14[/color]
[color=#ff8c00]=768 + 192 + 14[/color]
[color=#ff8c00]=960+14[/color]
[color=#ff8c00]=974[/color]
[color=#ff8c00][/color]
[color=#ff8c00][/color][color=#ff8c00]至於轉2進制可以考慮除得盡既2既最大倍數,[/color]
[color=#ff8c00]e.g.[/color]
[color=#ff8c00]974=512+462[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =512+256+206[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =512+256+128+78[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =512+256+128+64+14[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =512+256+128+64+8+4+2[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =2^9+2^8+2^7+2^6+2^3+2^2+2^1[/color][color=#ff8c00]  [/color]
[color=#ff8c00]  =1111001110(2進)[/color]

§黑紫● 2018-11-5 01:36 AM

[quote]原帖由 [i]ppresent[/i] 於 2018-11-4 04:28 PM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=490014742&ptid=27820074][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
974 = 16(60)+14 (14在16進制是E)
60= 16(3)+12 (12在16進制是C)
974(10進) = 3CE(16進)

Checking:
3*16^2+12*16+14
=3(256) + 192 + 14
=768 + 192 + 14
=960+14
=974

至於轉2進制可以考慮除得盡既2既最大倍數,
e.g.
974=512+462 ... [/quote]


Many thanks
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