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\(A=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(\sqrt{2}A=\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
\(\sqrt{2}A=\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1}\)
\(\sqrt{2}A=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(\sqrt{2}A=\sqrt{5}+1+\sqrt{5}-1=2\sqrt{5}\)
\(\Rightarrow A=\sqrt{10}\).
\(A=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(\sqrt{2}A=\sqrt{2}\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)\)
kĩ thuật nhân thêm \(\sqrt{2}\)( TH khi ko thể biến biểu thức trong căn thành HĐT, mà mình nhớ cách này được học đầu năm rồi mà ? )
\(=\sqrt{2}\sqrt{3-\sqrt{5}}+\sqrt{2}\sqrt{3+\sqrt{5}}\)
\(=\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)( đưa căn 2 vào căn nhớ bình phường nhé ! )
\(=\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}+1}+\sqrt{\left(\sqrt{5}\right)^2+2\sqrt{5}+1}\)
\(=\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}\)
\(=\left|\sqrt{5}-1\right|+\left|\sqrt{5}+1\right|\)
Vì 1 < 5 hay \(\sqrt{1}< \sqrt{5}\Rightarrow\sqrt{5}-1>0\)
\(\sqrt{5}>0;1>0\Rightarrow\sqrt{5}+1>0\)
\(=\sqrt{5}-1+\sqrt{5}+1=2\sqrt{5}\)
Vậy \(\sqrt{2}A=2\sqrt{5}\Rightarrow A=10\)
gọi số công nhân ban đầu là x
số lượng sản phẩm mỗi người phải làm là 120/x
sau đó 2 công nhân được điều đi làm việc khác và mỗi công nhân phải làm thêm 16 sp
=> (x-2)(120/x+16) = 120
<=> 16x2 - 32x - 240 = 0 ( tự giải đi nhé, mình không có máy tính :> )
đk: \(x\ge\frac{-7}{3}\).
pt tương đương với: \(3x^2+3x-3x\sqrt{3x+7}-4x+4+4\sqrt{3x+7}+x\sqrt{3x+7}+\sqrt{3x+7}\)\(-3x-7=0\)
\(\Leftrightarrow3x\left(x+1-\sqrt{3x+7}\right)-4\left(x+1-\sqrt{3x+7}\right)+\sqrt{3x+7}\)\(\left(x+1-\sqrt{3x+7}\right)=0\)
\(\Leftrightarrow\left(x+1-\sqrt{3x+7}\right)\left(3x-4+\sqrt{3x+7}\right)=0\)
Ta có: \(\sqrt{3x+7}=x+1\Leftrightarrow\hept{\begin{cases}3x+7=\left(x+1\right)^2\\x\ge-1\end{cases}}\Leftrightarrow x=3\)
\(\sqrt{3x+7}=4-3x\Leftrightarrow\hept{\begin{cases}3x+7=\left(4-3x\right)^2\\\frac{-7}{3}\le x\le\frac{4}{3}\end{cases}\Leftrightarrow x=\frac{3-\sqrt{5}}{2}}\)
Vậy...
ĐK: \(0\le x\le1\).
\(A=\sqrt{1-x}+\sqrt{1+x}+2022\sqrt{x}\)
- \(\sqrt{1+x}\ge\sqrt{1+0}=1\)
- \(\left(\sqrt{1-x}+\sqrt{x}\right)^2=1-x+x+2\sqrt{1-x}\sqrt{x}=1+2\sqrt{x\left(1-x\right)}\ge1\)
\(\Rightarrow\sqrt{1-x}+\sqrt{x}\ge1\)
- \(2021\sqrt{x}\ge0\)
Suy ra \(A\ge1+1+0=2\)
Dấu \(=\)xảy ra khi \(x=0\).
\(x^2-mx-3=0\)
\(\Delta=m^2+12>0\)nên phương trình luôn có hai nghiệm phân biệt \(x_1,x_2\).
Theo định lí Viete ta có:
\(\hept{\begin{cases}x_1+x_2=m\\x_1x_2=-3\end{cases}}\).
\(\left(x_1+6\right)\left(x_2+6\right)==2019\)
\(\Leftrightarrow x_1x_2+6\left(x_1+x_2\right)+36=2019\)
\(\Rightarrow-3+6m+36=2019\)
\(\Leftrightarrow m=331\)..
Exercise 1: Put the verbs in the brackets in the correct tense 1. If I had a typewriter, I ............would type.............(type) it myself. 2. If I ............knew.............(know) his address, I'd give it to you. 3 .He ............would look.............(look) a lot better if he shaved more often. 4. If you .............played............(play) for lower stakes, you wouldn't lose so much. 5. If he worked more slowly, he .........wouldn't make................(not make) so many mistakes. 6. I shouldn't drink that wine if I ...........were..............(be) you. 7. More tourists would come to this country if it ............had.............(have) a better climate. 8. If I were sent to prison, would you .............visit............(visit) me? 9. If someone ..........gave...............(give) you a helicopter, what would you do with it? 10. I ...............would buy..........(buy) shares in that company if I had some money. Exercise 2: Using the given information, make conditional sentences with IF 1. They are poor, so they can’t help us. → If they .............................weren't poor, they could help us...................................................................... 2. He doesn’t do his homework. He is always punished. → If he ..................................did his homework, he wouldn't be always punished...................................................................
3. He doesn’t have enough time. He can’t help me. → If he .........................................had enough time, he could help us............................................................. 4. She doesn’t take any exercise, so she is overweight. → If she ........................................took some exercises. she wouldn't be overweight............................................................ 5. He doesn’t have a bicycle, so he always goes to class late. → He wouldn’t ........................................go to class late if he had a bicycle................................................... 6. I am bad at English, so I can’t do homework. → I could .........................................do homework if i were bad at english.......................................................... 7. He doesn’t practise speaking French, so he doesn’t speak it fluently. → If he .............................................practised speaking english french, he would speak it fluetly.......................................................... 8. The meeting can be cancelled because it snows heavily. → If it ......................................didn't snow heavily, the meeting couldn't be cancelled............................................................... 9. We don’t go because it will rain. → If it ..................................didn't rain, we would go ...................................................................... 10. John is fat because he eats so many chips. → If John .......................................didn't eat so any chips, he wouldn't be fat...........................................................
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