快考试了,数学机经题求教!

Bessie2002

请各位大侠帮忙指点一下解题方法,谢谢!

(1)1/x^2+x^2=12, 求1/x^4+x^4=?

(2)有两个包，第一个里有2个红球，四个白球，第二个里有3个红球，五个白球，问每一个包中取一个球，全是白球的概率是多少；
1-C(2,2)C(3,3)/C(6,1)C(8,1)对吗?

(3)一个大等腰三角形内套一个小等腰三角形，两三角形共用一个底边，其中小三角形的两条腰是大三角形两个底角的角平分线。先给出小三角形的顶角W度数，求大三角行的顶角度数。

(4)A task is expected to be finished in 240 hrs, actually in 30% of the expected hrs finish ¼ of the task, the rate remains the same for the rest of the task, what is the fraction of how many more hrs spentand the expected hrs?

(5)Tax T is levied on profit P of the Nth month if P is over $5000 by the formula: T=P+N^1/2.What is the profit of September?
A. T-Sep. is over T-Apr. $4000
B. T-Sep. is over T-Jan. $2000
Answer??

(6)Do integers P and T have the same number of primer factors?
(1) P = 5 / 7 T
(2) P * T = 105
Answer:A??
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khe01

（1）1/x^2+x^2=12-----(1/x^2+X^2)^2=12*12-----1/x^4+x^4=144-2=142
(2) C41/C61*C51/C81=5/12
(3)设小三角形底角为X，大三角顶角为Y， 则2X+w=180 AND 4X+ Y=180-----求解。
（4）答案是20%
（5）E。（不确定）
（6）A。看一看“关于质因子讨论的文章”。如果问的是“相同数目的质因子”选A。 但如果问的是相同数目的不同的质因子，选C。

请大牛们指正。

[em12]

[此贴子已经被作者于2002-7-26 17:45:03编辑过]

tongxun

同意khe01的答案。

vancouver

以下是引用khe01在2002-7-26 17:45:03的发言：
(6)Do integers P and T have the same number of primer factors?
(1) P = 5 / 7 T
(2) P * T = 105

（6）A。看一看“关于质因子讨论的文章”。如果问的是“相同数目的质因子”选A。 但如果问的是相同数目的不同的质因子，选C。 

请大牛们指正。

[em12]

[此贴子已经被作者于2002-7-26 17:45:03编辑过]

I think C can never be a choice. Because

if (1) P = 5 / 7 T
   (2) P * T = 105
we have (5/7)* (T^2)=105
therefore, T=7(3)sq root, which is not an integer at all.

eleanor

6)Do integers P and T have the same number of primer factors?
(1) P = 5 / 7 T
(2) P * T = 105
If we do not consider whether the prime factors are same or not, then the answer is D
If we consider the same number of different prime factors, then it should be B

B is always true because P, and T are integers and 105 is composed of three prime factors, 3,5,7. So it determines that P and T can not have the same prime factor.

redpot

I agree with eleanor.