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• Chart Equation Mathematics 1 Part1 [Equations and Inetheles]    Toshikazu Sunada (Written by) Zuken Publishing Co., Ltd. (Publishing House) 2003April 1, 2016 (Release date) Hardcover (Format) Good、I'm going to start this collection of questions today~。 Let's start with Chapter 1, "Equations and Inequalities"。 Question 1、It is said that it is a problem of Doshisha Women's University。 This is just a matter of expanding the expression。 It's a hassle to calculate.。 \({ x }^{ 5 }\)The coefficient of is (-19\)、\({ x }^{ 3 }\)The coefficient of is (-23\)だろう。 ほい、正解～。 According to the commentary、全部を展開しなくてもその次数の項にだけ注目すればいいみたい、I see。 次は第2問。 同志社大の問題だ。 (1)は条件式から $$xyz=3\left( xy+yz+xz \right)\tag{1} $$ となり、あとは普通に与えられた式を展開して(1)式を代入すれば、都合よく\(\left( xy+yz+xz \right)\)section disappears and the answer comes out。 (2)According to the hint、 $${ x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }-3xyz=left( x+y+z right) \left( { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }-xy-yz-zx right) $$ It seems to use the formula that。 If we transform this equation into、 $${ x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ \left( x+y+z right) }^{ 3 }-3\left( x+y+z right) \left( xy+yz+zx \right) +3xyz $$ このようになって、The rest(1)と同様に式を代入すれば\({ x }^{ 3…
• (>_ Wikipedia (The free encyclopedia)The early Showa era (Date) うわごとのとなり赤マントは復活するか 現代の怪談ばなし - Folk room - And I was a long time ago. | フジパンシステム創成学科とは | 東京大学工学部システム創成学科 魔都東京。未解決事件おばけがやって来る。
• Chart Type Mathematics A part2 [Several In Case] Takaaki Yanagawa (Written by)Zuken Publishing Co., Ltd. (Publishing House)2003April 1, 2016 (Release date)Hardcover (Format) 今日も場合の数の問題を解いていくぞ～問6からだ。Oh well、It's a matter of combinations and circular permuting.。Different(n\)個のものの円順列の総数は\(\left( n-1 \right) !\)represented by。You can use this to solve it.。 And question 7。I made a mistake in this problem.。(1)、(2)Both、simply right four、I calculated it as a permutable to sort the top four.。By the way、Permutables that contain the same are represented by the following formula:。\(n\)Out of 10、同じものがそれぞれ\(p\)Pieces、\(q\)Pieces、\(r\)When there is one、これらを\(n\)What is the total number of permutables to be arranged?、 $${ _{ n }{ C }_{ P }\times }{ _{ n-p }{ C }_{ q }\times }{ _{ n-p-q }{ C }_{ r }=\frac { n! }{ P!q!r! } }\quad \left( p+q+r=n \right) $$ But、Now we're going to find a rectangular path.。This route is in the shape of a triangle.。 According to the answer example(1)3 squares sideways as a temporary road、Think of a three-square-length rectangular path。And、Point C、D、E、They set an F。And then、The path from point C to point D is right 3.、Because it is a permuting of the top three、it's officially required earlier。The rest is an extra route.、(Route through point E)\(+\)(Route through point F)\(-\)(Path through points E and F together)seeking as、It's good to pull.。Hmm.、I see. (2)It's hard to do it all the time.。Point P according to the answer example、Q、R、Establish S。and divided in the following four cases。 Pを通る経路 Qを通り、Pを通る経路 Rを通り、Qを通らない経路 Sを通り、Rを通らない経路 このようにすると、They are so、It's like it counts without duplication.。I didn't know this.。If the problem of such a route is focused on which point to pass, should it be parted?。 Next is Question 8.。6It's a matter of how to get on a boat that can take up to four people.。When distinguishing people、If you don't and you want to distinguish a boat、ask for four combinations if you don't。(1)if you don't distinguish between people and boats.、Only the number of people who share as hinted at is a problem.。(4)The (3)\(\div 2!\)It's like it's to。I solved it by the case、The answer became the same.。Well, I guess that's the way it is.。 Next is Question 9.。(1)is a matter of simple combinations。But、As for me(2)、(3)I made this wrong again.。"Is it a duplicate combination problem?" I thought, "I'm not going to do that."、It was a duplicate permuting problem.。ちなみに重複組合せで\(n\)個の異なるものから重複を許して\(r\)個をとる組合せの数は\({ _{ n+r-1 }{ C }_{ r } }\)represented by。\(n-1\)個の仕切りと\(r\)it's the number of permutings of 0 pieces.。Duplicate permuting, on the other hand,、Different(n\)個のものから重複を許して\(r\)In permuting to take out the pieces、\({ n }^{ r }\)required in。(2)It's easy to use.、(3)even if you're not(2)If you pull from, you will be asked。分からなかったな～ 最後に問10。It's a binary theorem problem.。二項定理とは\({ \left( a+b \right) }^{ n }\)の展開式の一般項（第r+1番目の項）が\({ _{ n }{ C }_{ r } }{ a }^{ n-r }{ B }^{ r }\)is to be written with。(1)You can use this to solve it.。(2)According to the hint, it seems to be good as follows。\({ x }^{ k }\)の係数を\({ a }_{ k }\)They go to。そして\(\frac…