① {#mathml#}$\sqrt{2}${#/mathml#} ﹣1与2﹣ {#mathml#}$\sqrt{3}${#/mathml#} ；②2﹣ {#mathml#}$\sqrt{3}${#/mathml#} 与 {#mathml#}$\sqrt{6}${#/mathml#} ﹣ {#mathml#}$\sqrt{5}${#/mathml#} ；

（Ⅱ）类比以上结论，写出一个更具一般意义的结论，并给出证明．

① {#mathml#}$\sqrt{2}${#/mathml#} ﹣1与2﹣ {#mathml#}$\sqrt{3}${#/mathml#} ；②2﹣ {#mathml#}$\sqrt{3}${#/mathml#} 与 {#mathml#}$\sqrt{6}${#/mathml#} ﹣ {#mathml#}$\sqrt{5}${#/mathml#} ；

（Ⅱ）类比以上结论，写出一个更具一般意义的结论，并给出证明．

阅读下面短文, 从短文后各题所给的四个选项(A、B、C、D)中, 选出可以填入空白处的最佳选项。

    The day finally came, when I had to leave the warm home where I'd grown up. I ran to the back yard, as tears came up from my heart. Suddenly I 1 a hand rest on my shoulder. I looked up to 2  my grandfather. “It isn't 3 , is it, Billy?” he said softly.

    He gently 4  my hand in his, and then we walked, hand in hand, to the front yard, 5 a huge red rose-bush sat alone.

    “What do you see here, Billy?” he asked. I looked at the flowers, not knowing 6  to say, and then answered, “I see something soft and 7 ,  Grandpa.”

    He pulled me 8 . “It isn't just the roses that are beautiful, Billy. It's that special place in your heart that makes them so.” “Billy, I 9 these roses when my first son was born. It was my 10  of saying ‘thank you' to God. I 11 to watch him pick roses for his mother. Then, as a young man of only 20, a terrible war robbed him of his life.” Grandpa slowly stood up. “Never say good-bye, Billy. Never 12  to the sadness and the loneliness. Instead, I want you to remember the joy and the 13  when you first said hello to a friend.”

    A year later, my grandpa became very 14 . Then all members of the family were 15  back, and I returned to the old house. When it came to my 16 , I took his hand as 17  as he had once taken mine.

    “Hello, Grandpa,” I 18 . His eyes slowly opened and said, “Hello, my friend.” With a brief (短迅的) 19  he died. Suddenly, and truly, I knew what he had 20  about never saying good-bye — about refusing to give in to sadness.

根据短文理解，选择正确答案。

    Our love of music and appreciation of musical harmony (和声) is learnt and not based on natural ability, a new study by University of Melbourne researchers has found. The researchers said previous theories about how we appreciate music were based on the physical functions of sound, the ear itself and a born ability to hear harmony.

    The study shows that musical harmony can be learnt, and it is a matter of training the brain to hear the sounds. So if you thought that the music of some foreign culture (or Jazz) sounded like the crying of cats, it's simply because you haven't learnt to listen by their rules.

    The researchers used 66 volunteers with a range of (一系列的) musical training and tested their ability to hear combinations (组合) of notes (音符) to determine if they found the combinations familiar or pleasing. They found that people needed to be familiar with combinations of notes. If they couldn't recognize the notes, they found the notes dissonant. This finding put an end to centuries of theories claiming (声称) that physical functions of the ear determine what we find attractive.

    The study found that trained musicians were much more sensitive (敏感的) to unpleasant notes than non-musicians. When they couldn't find the note, the musicians reported that the sounds were unpleasant, while non-musicians were much less sensitive. This shows the importance of training or nurturing (培养) the brain to like particular sound of combinations of notes, like those found in jazz or rock.

    Depending on their training, a strange chord (和弦) sound was pleasant to some musicians, but very unpleasant to others. This showed us that even the ability to hear a musical note is learnt.

    To confirm (证实) this finding, they trained 19 non-musicians to find the notes of a random (随机的) selection of western chords. Not only did the participants' ability to hear notes improve rapidly; the chords they had learnt sounded more pleasant—regardless of (不论) how the chords were played.

    The question of why some combinations of musical notes are heard as pleasant or unpleasant has long been debated. “ We have shown in this study that for music, beauty is in the brain of the beholder(观看者),” a researcher said.

根据短文理解，选择正确答案。

    Grammar is the system of a language. People sometimes describe grammar as the “rules” of a language; but in fact no language has rules. If we use the word “rules”, we suggest that somebody created the rules first and then spoke the language, like a new game. But languages did not start like that. Languages started by people making sounds which evolved (逐渐发展成) into words, phrases and sentences. No commonly-spoken language is fixed. All languages change over time. What we call “grammar” is simply a reflection (反映) of a language at a particular time.

    Do we need to study grammar to learn a language? The short answer is “no”. Very many people in the world speak their own, native language without having studied its grammar. Children start to speak before they even know the word“grammar”. But if you are serious about learning a foreign language, the long answer is “yes, grammar can help you to learn a language more quickly and more efficiently.” It's important to think of grammar as something that can help you, like a friend. When you understand the grammar (or system) of a language, you can understand many things yourself, without having to ask a teacher or look in a book.

    So think of grammar as something good, something positive, something that you can use to find your way---like a signpost(路标) or a map.

    Except invented languages like Esperanto（世界语）. And if Esperanto were widely spoken, its rules would soon be very different.

根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。

    Using too much water or throwing rubbish into our rivers are clear ways that humans can put our water supply in danger, but we also affect our water supply in less obvious ways. You may wonder how paving (铺砌) a road can lead to less useable fresh water. {#blank#}1{#/blank#} Groundwater does not come from lakes or rivers. It comes from underground. The more roads and parking lots we pave, the less water can flow into the ground to become groundwater.

    {#blank#}2{#/blank#} Drier climates are of course more likely to have droughts（干旱）than areas with more rainfall, but, in any case, good management can help to make sure there is enough water to meet our basic needs.

    {#blank#}3{#/blank#} In the United States, a family of four can use 1.5 tons of water a day! This shows how much we depend on water to live, but there's a lot we can do to lower the number.

    {#blank#}4{#/blank#} To start with, use the same glass for your drinking water all day. Wash it only once a day. Run your dishwasher (洗碗机) only when it is full. {#blank#}5{#/blank#} You can even help to keep our water supply clean by recycling (回收) batteries instead of throwing them away.

A. Human activity is not responsible for all water shortages.

B. Help your parents fix any leaks (漏水的地方) in your home.

C. Thinking about the way we use water every day can make a big difference, too.

D. Some measures to save water should be taken by the government.

E. A major part of the water we use every day is the water from lakes or rivers.

F. A major part of the water we use every day is ground water.

G. You can take steps to save water in your home.

The family {#blank#}1{#/blank#} (be) sitting at the breakfast table.