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Ex1
1 an - the
2 a - a
3 a - the
4 an - 0
5 The
Ex2
1 đúng
2 an - 0
3 a
4 a - the
5 the - a
Ex3
1 a => the
2 a => the
3 doctor => a doctor
4 đúng
5 đúng
Bạn đăng câu hỏi ở 1 diễn đàn thoi nhé, hai diễn đàn có liên kết ạ
Ta có : a chia 6 dư 2 => a - 2 chia hết cho 6 => a - 2 + 12 chia hết cho 6 => a + 10 chia hết cho 6
a chia 7 dư 4 => a - 4 chia hết cho 7 => a - 4 + 14 chia hết cho 7 => a + 10 chia hết cho 7
=> a + 10 chia hết cho 6 và 7
=. a + 10 thuộc BC ( 6 ; 7 )
Mà BCNN ( 6 ; 7 ) = 42
=> a + 10 thuộc B ( 42 ) = { 0 ; 42 ; ... }
=> a + 10 chia 42 dư 42
=> a chia 42 dư 32
Vậy số a chia cho 42 dư 32
\(\dfrac{4}{x}+\dfrac{2}{y}=1\) \(\left(x;y\ne0\right)\)
\(\Rightarrow2x+4y=xy\)
\(\Rightarrow2x-8+4y-xy=-8\)
\(\Rightarrow2\left(x-4\right)-y\left(x-4\right)=-8\)
\(\Rightarrow\left(x-4\right)\left(y-2\right)=8\)
\(\Rightarrow\left(x-4;y-2\right)\in U\left(8\right)=\left\{-1;1;-2;2;-4;4;-8;8\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(3;-6\right);\left(5;10\right);\left(2;-2\right);\left(8;4\right);\left(-4;;1\right);\left(12;3\right)\right\}\)
Với mọi x;y;z ta có:
\(\left\{{}\begin{matrix}\left(x-2\right)^2\ge0\\\left(y-2\right)^2\ge0\\\left(z-2\right)^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-1\right)^2+\left(y-1\right)^2+\left(z-1\right)^2\ge0\)
\(\Rightarrow x^2+y^2+z^2\ge4\left(x+y+z\right)-12\) (1)
Đồng thời cũng có:
\(\left\{{}\begin{matrix}\left(x-y\right)^2\ge0\\\left(y-z\right)^2\ge0\\\left(z-x\right)^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2\ge0\)
\(\Rightarrow2\left(x^2+y^2+z^2\right)\ge2\left(xy+yz+zx\right)\)
\(\Rightarrow4\left(x^2+y^2+z^2\right)\ge4\left(xy+yz+zx\right)\)(2)
Cộng vế (1) và (2):
\(\Rightarrow5\left(x^2+y^2+z^2\right)\ge4\left(x+y+z+xy+yz+zx\right)-12=4.18-12=60\)
\(\Rightarrow x^2+y^2+z^2\ge\dfrac{60}{5}=12\)
Dấu "=" xảy ra khi \(x=y=z=2\)
Ex. 11 :
1. take -> takes
2. never is -> is never
3. waking -> wakes
4. has been -> was
5. will go -> go
6. aren't -> isn't
7. interested on -> interested in
8. as well as -> as soon as
9. keen into -> keen on
10. is -> are
11. telling -> to tell
12. what happened -> what had happened
13. was keen about -> was keen on
14. probably will -> will probably
15. will -> will be
Ex.12 :
1. I'm keen on maths.
2. Unless you listen, you won't follow the teacher's lecture.
3. We are interested in walking in the rain
4. Should you ask me for the car, i will lend it to you.
5. John spends 30 minutes to walk to school.
6. She's fond of playing cards with her children at the weekend.
7. She's interested in taking photos of her children.
8. We don't have any time to prepare the speech.
9. I promise I will phone you next week.
10. I am fond of watching the goldfish in the tank.
11. My mon isn't passionate about preparing meals.
12. He fancies reading comic books.
13. I think not many people are into listening to music in their free time.
14. Should he studies hard, he will pass the exam.
15. If you go out in the rain, you will get wet.
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