equation既問題

小霞的fans · 發表於 17/2/2010 03:07 PM

近來開post開得好密><希望大家原諒~

suppose a and b are the roots of the equation 10x^2-20x+1 = 0
without solving the above equation , find the value of

a)4^a x 4^b ,

b)loga + logb

唔solve條式點搵a 同 b既值呢,,thx~

sapphire · 發表於 17/2/2010 04:04 PM

For this kind of question, it is not necessary to solve a and b.

a + b = 20/10 = 2
ab = 1/10

(a) 4^a * 4^b = 4^(a + b)
(b) log(a) + log(b) = log(ab)
and do the calculation......

Actually, when you see this kind of question (without finding the roots), you may think about the sum of root and the product of root.

小霞的fans · 發表於 17/2/2010 04:23 PM

For this kind of question, it is not necessary to solve a and b.

a + b = 20/10 = 2
ab = 1/10

(a) 4^a * 4^b = 4^(a + b)
(b) log(a) + log(b) = log(ab)
and do the calculation......

Actually, ...
sapphire 發表於 16/2/2010 08:04 PM

點解a + b = 20/10 = 2 既!?
糟糕,,我咁基本都唔識 .....

ice · 發表於 17/2/2010 04:38 PM

點解a + b = 20/10 = 2 既!?
糟糕,,我咁基本都唔識 .....
小霞的fans 發表於 17/2/2010 04:23 PM

因為sum of roots = -b/a (ax^2+bx+c)

小霞的fans · 發表於 17/2/2010 05:15 PM

因為sum of roots = -b/a (ax^2+bx+c)
IceDragon 發表於 16/2/2010 08:38 PM

@[]@而家先知有呢條式,,上堂冇用過呢條式
仲有其他式的嗎?

unlock-YM · 發表於 17/2/2010 05:19 PM

@[]@而家先知有呢條式,,上堂冇用過呢條式
仲有其他式的嗎?
小霞的fans 發表於 17/2/2010 05:15 PM

A Maths的... 基本上冇讀過就唔會識。(唔知現時CE Maths syllabus有冇)

ice · 發表於 17/2/2010 05:22 PM

@[]@而家先知有呢條式,,上堂冇用過呢條式
仲有其他式的嗎?
小霞的fans 發表於 17/2/2010 05:15 PM

仲有product of roots = c/a (這個你應該懂了)
delta = b^2-4ac
delta>0 = 2 distinct real roots
=0 = 2 equal real roots
<0 = unreal roots
大概就這些了

Luna · 發表於 17/2/2010 06:15 PM

A Maths的... 基本上冇讀過就唔會識。(唔知現時CE Maths syllabus有冇)
unlock-YM 發表於 17/2/2010 05:19 PM

334學生表示中四上學期教了
p.s.是core syllabus

unlock-YM · 發表於 17/2/2010 06:56 PM

8# Luna

334? 咁我完全唔會懷疑... 聽聞更有complex number。

Sorry 版主，好似click錯報告，但係搵唔到點delete已發送pm，唔多熟呢個Discuz!版本。

hk56740 · 發表於 17/2/2010 11:11 PM

9# unlock-YM
冇錯呀,334 compulsory maths的確要讀complex no.同sum and product of root,仲有heron's formula

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