✔ 最佳答案
1.解(2x2－4x＋1)(5x2－10x＋2)－24＝0
解：原式 ==>
[2(x2-2x)+1][5(x2-2x)+2]-24=0
10(x2-2x)2+9(x2-2x)-22=0
[10(x2-2x)-11][(x2-2x)+2]=0
(10x2-20x-11)(x2-2x+2)=0
x=(5+-√ 55)/5 or 1+-i
2.(x2＋5x＋6)(x2＋20x＋96)－4x2＝0
解：原式==>
(x+2)(x+3)(x+12)(x+8)-4x2=0
(x2+14x+24)(x2+11x+24)-4x2=0..........找乘積木同合併
(x2+24)2+25(x2+24)x+150x2=0
(x2+24+15x)(x2+24+10x)=0
x=-4 or -6 or (-15+-3√ 14)/2
3.(x2＋2/x2＋4x＋1)＋(x2＋4x＋1/x2＋2)＝5/2
解：令t=(x2+2)/(x2+4x+1)
原式==>t+(1/t)=5/2
2t2-5t+2=0
t=2 or 1/2
(1)當t=2時==>(x2+2)/(x2+4x+1)=2
==>x2+8x=0==>x=0 or -8
(2)(1)當t=1/2時==>(x2+2)/(x2+4x+1)=1/2
==>x2-4x+3=0==>x=1 or 3
4.(x＋3/3－x)＋(x＋6/6－x)＋(x＋9/9－x)＝3
解：原式==>
(x+3)/(x-3) +(x+6)/(x-6) +(x+9)/(x-9)+3=0
[1+ 6/(x-3)]+[1+ 12/(x-6)]+[1+ 18/(x-9)]+3=0
==>1/(x-3) +2/(x-6) + 3/(x-9) +1=0
==>(x-6)(x-9) +2(x-3)(x-9) +3(x-3)(x-6)+(x-3)(x-6)(x-9)=0
==>6x2-66x+162+x3-18x2+99x-162=0
==>x3-12x2+33x=0
==>x(x2-12x+33)=0
==>x=0 or 6+-√ 3
5.矩形長ι,寬ω,且ι/ω＝2ω/ι－ω,試求ι/ω＝?
解：令t=l/w
l/w=2/(l/w -1) ==>t=2/(t-1) ==>t2-t-2=0
==>t=2 or -1
故l/w= 2 or -1
2008-07-15 15:35:19 補充：
訂正：
5.哈！太累了，所以沒驗算！
第 5題 l/w=2 or -1(不合)
第2題x^2+15x+24=0
==>x=(-15+-√129)/2
2008-07-15 15:36:29 補充：
sponge ：謝謝你的驗算！
是的，昨晚因看這題沒人做，所以做了一下，也沒驗算！
