[SOS!!]F.4 math [複製鏈接]

引用第19樓eeeex於2009-12-12 21:24發表的  :
α+β= -b/a
αβ=c/a
你有無計錯-.-

應該是用錯方法

轉中文搵波仔

1. null

引用第2樓牙銓於2009-12-12 20:02發表的  :
(-13)^2-4(1)(R)=0
169-4R=0
R=42.25
x^2-13x+42.25=0
13+/-開方根(-13)^2-4(1)(42.25)開方根
.......

no real roots , deta < 0
two distinct real roots , deta > 0
onedubble real root , deta = 0
條式應該係 R < 42.25
另外想講R應該搵唔到的- -
一係比漏左資料
只係比左兩個roots
計出黎,應該係 b=169-2R

如果ans = 125
咁R = 22

引用第21樓623於2009-12-13 00:56發表的  :
轉中文搵波仔

p 同 q 係方程 x²-13x+R 的解
而R是一個實數
b = p²+q²                                       即是 =  [ (p+q)² - 2pq ]
試找出b 的數值

simple- -
as p+q =13 and p , q are prime
only 1 combination is true
is 2 and 11- -
p²+q² = 11² + 2² = 125

remark  :
if a ,b , c are positive integers and satisfies
a² + b² = c²
then at least one of a , b is even

引用第23樓~瘋人~於2009-12-13 01:36發表的  :
simple- -
as p+q =13 and p , q are prime
only 1 combination is true
is 2 and 11- -
p²+q² = 11² + 2² = 125
.......

怒我愚昧
p同q點解一定會係2同11= =?
10同3呢?

引用第24樓牙笨於2009-12-13 13:23發表的 :
怒我愚昧
p同q點解一定會係2同11= =?
10同3呢?

prime

引用第25樓~瘋人~於2009-12-13 13:30發表的  :
prime

1. 最初的;原始的;基本的;原有的
a prime source of information
信息的最初來源
2. 主要的;首位的
The community's prime need is a new school.
這個社區的第一需要是一所新學校。
3. 最好的,第一流的
The show was on television during prime time, when everyone was watching.
這節目在黃金時間播映,這時大家都在看電視。
4. 青春的;血氣方剛的
5. 【數】質數的,素數的
n.
1. 最初,初期[the S]
2. 黎明;春天[the S]
the prime of the year
春季
3. 青年;壯年;全盛時期[the S]
He died in the prime of his life.
他在壯年時死去。
4. 精華,最好部分[the S]
5. (常大寫)晨經,晨禱[the S]
6. 【數】質數,素數[C]
vt.
1. 灌注,裝填;為...裝火藥(或雷管)
The gun was primed and ready.
這砲已裝上火藥,準備就緒。
2. (注水或油等)使起動[(+with)]
3. 在...上塗底漆(或底色)
You must prime the wood before you paint it.
油漆這木製東西前,你得先在上面塗上底漆。
4. 使準備好
5. 事先給...指導;事先為...提供消息(或情報等)[(+with)]
The man on trial had been carefully primed by his lawyer.
這個受審人已得到他律師的仔細指點。
vi.
1. 作準備


prime = roots?

prime = 質數

有條M.I唔識....
If prove that
1x2x2+2x3x4+....+n(n+1)(2n)=n(n+1)(n+2)(3n+1)
                                                     -------------------------
                                                                      6

evaluate the following expressions:
8x16x18+9x18x20+....+18x36x38

引用第23樓~瘋人~於2009-12-13 01:36發表的  :
simple- -
as p+q =13 and p , q are prime
only 1 combination is true
is 2 and 11- -
p²+q² = 11² + 2² = 125
.......

謝大人幫忙

引用第28樓yhmjack1於2009-12-13 14:38發表的 :
有條M.I唔識....
If prove that
1x2x2+2x3x4+....+n(n+1)(2n)=n(n+1)(n+2)(3n+1)
                                                     -------------------------
                                                                      6
.......

Let P(n) be the proposition 1x2x2+2x3x4+....+n(n+1)(2n) = n(n+1)(n+2)(3n+1)/6

when n = 1
L.H.S = 4
R.H.S = 1(1+1)(1+2)(3+1)/6 = 4

as L.H.S = R.H.S
P(1) is true

Assume P(k) is true for some positive integers k

1x2x2+2x3x4+....+k(k+1)(2k) = k(k+1)(k+2)(3k+1)/6

when n = k+1
L.H.S =1x2x2+2x3x4+....+k(k+1)(2k) + (k+1)(k+2)(2k+2)
           = k(k+1)(k+2)(3k+1)/6 + (k+1)(k+2)(2k+2)
           =(k+1)(k+2)[k(3k+1) + 12k+12]/6
           =(k+1)(k+2)(3k² + 13k + 12)/6
           =(k+1)(k+2)(3k+4 )(k+3 )/6

R.H.S=(k+1)(k+2)(k+3)(3k+4)/6

so L.H.S = R.H.S

By the principle of MI...................................

8x16x18+9x18x20+....+18x36x38

=2[8x9x16 + 9x10x18 +....18x19x36]
=2[1x2x2+2x3x4+....+18x19x36 - 1x2x2 +.....7x8x14]
=2 * [18(19)(20)(55)/6 - 7(8)(9)(25)/6]
=