求解設''a=√x+ 1/√x及b=√x- 1 /√x

2008-03-05 1:16 am
如題!!

求解設''a=√x+ 1/√x及b=√x- 1 /√x找出a和b的關係

回答 (2)

2008-03-05 1:34 am
✔ 最佳答案
a=√x+1/√x
a=(√x)+2(√x)(1/√x)+(1/√x)
a=x+2+1/x------(1)

b=√x- 1 /√x
a=(√x)-2(√x)(1/√x)+(1/√x)
b=x-2+1/x-------(2)

(1)-(2)
a-b=4



2008-03-04 17:35:58 補充:
修正~
a=√x+1/√x
a^2=(√x)^2+2(√x)(1/√x)+(1/√x)^2
a^2=x+2+1/x------(1)

b=√x+1/√x
b^2=(√x)^2+2(√x)(1/√x)+(1/√x)^2
b^2=x+2+1/x------(1)

(1)-(2)
a-b=4

2008-03-04 17:36:11 補充:
a^2-b^2=4

2008-03-04 19:46:54 補充:
TO lpssust:
你個答案好有問題
設x=4
a=√4+ 1/√4=2+1/2=5/2
b=√4- 1/√4=2-1/2=3/2
如果a = (√5/3 )b,
5/2=(√5/3 )(3/2)=(3√5)/(2√3)
不過(3√5)/(2√3)唔係等於5/2

我估你係以為(√x+1/√x)^2=x+1/x,(√x-1/√x)^2=x-1/x
先會有
a^2 + b^2 = 2x
a^2 - b^2 = 2/x
不過,
(m+n)^2=m^2+2mn+n^2唔係=m^2+n^2

我勸你唔好教錯人la!!

2008-03-04 20:01:27 補充:
小小補充
TO lpssust:
你做ge方法都係錯ga
a^2 + b^2 = 2x
a^2 - b^2 = 2/x
你只要將兩式相乘就得:
(a^2+b^2)(a^2-b^2)=2
a^4-b^4=2

不過e個答案都係錯

2008-03-05 17:54:49 補充:
就算你
a^2 + b^2 = 2x
a^2 - b^2 = 2/x
唔係錯,不過你都係做錯~
(a^2 + b^2)/2 = 2/ (a^2 - b^2)
(a^2 + b^2)(a^2 - b^2)=4
但係你係
(a^2 + b^2)/(a^2 - b^2)=4
中間冇除號ga!!
交叉相乘都唔識= =
參考: ME, me, me, me, me
2008-03-05 2:06 am
=>
a^2 + b^2 = 2x
a^2 - b^2 = 2/x

(a^2 + b^2)/2 = x
x = 2/ (a^2 - b^2)
=>
(a^2 + b^2)/2 = 2/ (a^2 - b^2)
=>
(a^2 + b^2)/(a^2 - b^2) = 4
=>
a^2 + b^2 = 4a^2 - 4b^2

=>
3a^2 = 5b^2
=>
a = (√5/3 )b





2008-03-04 23:10:14 補充:
如果唔係all over 既話

咁有乜必要用root x?

我個人覺得係問問題打唔曬成個出泥wow
anyway

其實最簡單就係sub 個4 去x 度
再睇返呢個答案arm

我冇乜所謂
多個意見o者


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