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数学 高校生

青チャートIIの不等式の証明の質問です。黄色線の様に(2)は何故aにa+b,bに-bを代入して良いんですか?青線の様に不等式の形が違うから(2)で「(1)の不等式で~」と使えなくないですか?

OO0。 (2), (3) (1)と似た形である。そこで,(1)の結果を利用することを考えるとよい。 指針> (1) 例題 28 と同様に,(差の式)20は示しにくい。 基本 例題29 絶対値と不等式 (3) la+b+c\<\a\+\bl+, 次の不等式を証明せよ。 (1) la+b|sla|+|b| (2) lal-|b|sla+b| 基本28 1AF=A°を利用すると,絶対値の処理が容易になる。そこで A20, B20のとき A2B→A2B'→A-B'20 CHART似た問題 1 結果を利用 2 方法をまねる 解答 4|AP=A° 4ab|=la|| 1(1)(la|+||)°-la+bf=q°+2la||6|+8-(a°+2ab+6°) =2(lab|-ab)20 la+ofs(la|+||)° よって la+b|20, la|+|6|20から 別解 一般に,-la|<aslal, -|b|sbs|b| が成り立つ。 この不等式の辺々を加えて 4この確認を忘れずに。 4A|2A, IA|2-Aから ーIA|SAS|A la+b|<la|+|b| ー(lal+||)Sa+bsla|+||| la+blsla|+|b| (2)(1)の不等式でaの代わりにa+6, bの代わりに-6と -BSASB →A|SB したがって イズーム UP 参照。 おくと よって Jalsla+b|+|| 別解 [1] lal-Tb<Oのどぎ la+b|20であるから,lal-|6|<la+b|は成り立つ。 [2] lal-|b|20 のとき la+bf-(lal-lb|)°=d+2ab+8-(α°-2|a|||+6°) ゆえに lal-|b|<|a+bl lal-|||<0sla+o [2] の場合は,(2)の左辺 右辺は0以上であるから、 (右辺)-(左辺)20を示 す方針が使える。 =2(ab+lab|)20 (lal-|6|0°<la+6? よって la|-|b|20, la+b|20であるから [1], [2] から lal-|b|<|a+b|

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英語 高校生

英語の長文です! わかる方お願いします

ロ文型/文の種類 社会 1 25 rh Chapter Time: 35 mnutes 1 英文を読んで、設間に答えなさい。 Most important easons for doing voluntecr work Number of hous students volunteered per month 1%of students help people or community 44% 104 eam something new 24% Sto 10 get work eperience 20% 11 or more other 12% St. Martin's High School conducts a survey of student volunteer work 。 every year. The survey results show that many students have positive atitudes toward volunteering. The graph above shows the average amount of time that students spent doing volunteer work per month in this year. The table s shows the most important reasons given for participating. The teachers at the school have encouraged their students to volunteer since 2009. Before then, few students did volunteer work. When Brian Amster, the present principal, first came to the school in 2008, he found that there was litle communication among students, their families, and the 10 Community. As St. Martin's High School was in a newly developed arca, more than half of the students and their families were newcomers, and they did not know cach other or the area very well. Mr. Amster thought this was not good for the students and the communiry. Mr. Amster came up with the idea of volunteer work. p He wanted his の 15 students to have more contact with the local people through helping those in need. The local people really welcomed the volunteer activities. Volunteering gave many students a chance to learn a lot, and their self-esteem improved. It was good for the community and the students themselves, too. Mr. Amster says, "In the beginning, most of the volunteer activities 4 20 involved helping old people. Today, however, more and more students are doing activities related to the environment, such as cleaning parks and other public areas. Parents are also encouraged to help, and cach year, more and more parents are participating." One thing that makes Mr. Amster especially proud is that most students continue voluntering even after graduation. さ

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