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Mathematics Senior High

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SUP PLY 88597- PE-M381-1/ITEM DOOO ) a, bは有理数とする。a+b/T =0 のとき, Vl が無理数であることを 用いて,6=0 であることを証明せよ。 (2)(1+/2)x+(-2+3/2)y=10 を満たす有理数x, yの値を求めよ。 9L 基本。 lOLUTION CHART (1) 直接がだめなら間接で 背理法 6キ0 と仮定して矛盾を導く。 (2)/2 について整理して,(1)の結果を利用する。このとき, 前提条件 「x, yは有理数, /2 は無理数」を書くことを忘れないよう注意。 解答 の(1) 6キ0 と仮定すると =1- 9 D 94 0= 1/9+D a, bは有理数であるから,右辺の-- 0 は有理数である。 Dー= = 1^9 左辺の、7 は無理数であるから,これは矛盾している。 2(0キ)9 VEE (2) 与式を変形して -=1 さす乗さ 2Cf 0=9 33 (x-2y-10)+(x+3y)/2=0 R 0… *この断りは重要。 x, yは有理数であるから, x-2y-10, x+3y は有理数であ り,(2 は無理数である。 ゆえに,(1)の結果から 2をOに代入して 2, ③ を解いて inf. 上の例題(1)において, b=0 を a+b\l =0 に代入すると a+0/I =0 から a=0 よって, a+b、T =0 のとき a=b=0 が成り立つ なお,「a, bは有理数」 という記述がないと, a+b、2 =0 を満たすa, bは E だけではなく, a=2(無理数), b=-1 なども適してしまう。 */2 について整理 詳しくは右ペー x+3y=0 の 0=0I-7-x x=6, y=-2 や心 *(x-2y-10)+0- から x-2y-I MOTAMSC INIO

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English Senior High

リードB持っている方不定詞のステップ1の解答送っていただけませんか? 学校で解答冊子持ってくるの忘れてしまって、。お願いいたします。

不定詞 STEP O 1(to-不定詞の名詞的用法·形容詞的用法·副詞的用法》 次の各文の to-不定詞が,名詞的用法 ならア,形容詞的用法ならイ,副詞的用法ならウと答えなさい。 (1) It is a pity to be indoors on a day like this. (2) Children go to school to learn things. (3) Iwant to buy a book oto read on the journey. 09 (4) Don't you think it wrong to tella lie to your friend? J0 J ( (5) His son grew up to be a very sociable man. (6) She had the courage to say no. (7) He must be a fool to act in that way. (8) There was no time for her to call on her aunt. 2(to-不定詞の名詞的用法〉 次の各文の to-不定詞の働きが,主語ならア, 目的語ならイ, 補語 ならウと答えなさい。 ena JD 9ge to forget all. (2) It is hard to criticize the people you like. To know all is Jの ( (3) I forgot to mail your letter. (4) Do you think it strange for me to live by myself? JpO pe 3(to-不定詞の形容詞的用法〉次の各文の下線部を to-不定詞を用いた形にして,全文を書きか えなさい。 (1) This is the best way of curing a cold. E 0~ ( ゆ) (2) He was the last person who left the office. DIg 2or (3) He has no friends who will support him. 1ore stgin (4) This apron has no pocket in which I can put things. 4(to-不定詞の副詞的用法〉 次の各文を[ ]内の指示に従って書きかえなさい。 (1) Her coach was disappointed when he heard of her failure. (下線部を to-不定詞を用いて) [only to ~ (2) We hurried to the house but found that it was empty. (21出孝 to ~を用いて) (3) This bag is so small that it cannot hold all these things. [too (4) This book is so easy that a six-year-old child can read it. [ enough to ~ を用いて) 語 注 no pocket in which I can put things 私がものを入れられるポケット(がない) 19

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TOEIC・English Undergraduate

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rom the information we obtained, we believe First Bank and Union Bank will (D) Judgment most Iikely merge to form the biggest bank in the country. (B) Judge (A) Judging (C) Judged Tou should bring your own laptop computer, since all the computers in the office out of order. (D) being (A) is (B) are (C) been to Rome to start her own business. (D) movement 13. Janet spent 10 years in Paris before (A) move (B) moves (C) moving the spreadsheet software. (C) are updated 14.I received an e-mail from SmartSoft and (A) updating (B) update (D) updated tA 15. Mr. Carlton is seeking a position as a bond analyst on Wall Street. (C) challenged (A) challenge (B) challenging (D) to challenge 16. in 1909, the Nara Hotel has been popular with celebrities from around the world (A) Establishes (B) Establishing (C) Established (D) Having establishe 17. Before you apply for the position, you need to have the application form supervisor. (A) signed .by your (B) sign (C) been signed (D) are signing A 18. Please to the attached file when you prepare the documents for the presentation. (A) refers (B) refer (C) referred (D) referringnie 19. her extensive knowledge of computer programming, Ms. Harris is the top candidate for the position. (A) Give (B) Giving (C) Having given 20. Mr. Peterson, the department manager, insisted that all employees (D) Given time. their work on (A) finish (B) has finished (C) finishingbnoo (D) finished

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