math questions Help!!!

[匿名]

2009-08-26 12:40 am

1)Factorize x^6 -1

2)a)factorize x^4 + x^2 +1 [hints:conpare with x^4+2x^2+1.]

b)factorize (x+1)^4 +(x+1)^2+1by using the result of(a)
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1)a wire of30cm long is divided into three parts in the ratio 4:5:6.find
the length of each part.
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圖http://us.f6.yahoofs.com/hkblog/njLcOQ6FBRQYG13ZuCFh6Q--_1/blog/20090825043214127.jpg?ib_____Db0YsGNmd
In the figure,AB=4cm ,CN=2.8cm ,A'B'=6cm andCN:MD =2:3 find
(a)the scale factor;
(b)MD;
(c)C'N' and M'D' and
(d)the area of A'C'B'D'

回答 (1)

用戶7639

2009-08-26 4:32 am

✔ 最佳答案

1)x6-1
=(x2)3-1
=(x2-1)(x4+x2+1)
=(x-1)(x+1) (x4+x2+1)

2)a) x4+x2+1
=x4+2x2+1-x2
=(x2+1)2-x2
=[(x2+1)-x] [(x2+1)+x]
=(x2-x+1)(x2+x+1)

b)(x+1)4 +(x+1)2+1
=[(x+1)2-(x+1)+1] [(x+1)2+(x+1)+1]
=[(x2+2x+1)-(x+1)+1][(x2+2x+1)+(x+1)+1]
=(x2+x+1)(x2+3x+3)

1) Let the length of each part of the wire be 4x,5x and 6x.
4x+5x+6x=30
15x=30
x=2
the length of each part=8cm,10cm and 12.

(a)4:6
(b)MD=3/2 CN
=3/2(2.8)
=4.2cm

(c) C’N’=6/4(2.8)
=4.2cm
M'D'=6/4(4.2)
=6.3cm

(d) the area of A'C'B'D'=1/2(6)(6.3)+1/2(6)(4.2)
=18.9+12.6
=31.5cm2

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