Hãy đặt 8 quân Hậu vào bàn cờ vua tiêu chuẩn sao cho không có quân Hậu nào tấn công được nhau. (màu của quân Hậu không có ý nghĩa trong trường hợp này)
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8x2y2+x2+y2=10xy8x2y2+x2+y2=10xy
⇔8x2y2−8xy+x2+y2−2xy=0⇔8x2y2-8xy+x2+y2-2xy=0
⇔2(4x2y2−4xy+1)+x2+y2−2xy=2⇔2(4x2y2-4xy+1)+x2+y2-2xy=2
⇔2(2xy−1)2+(x−y)2=2⇔2(2xy-1)2+(x-y)2=2
Nếu(2xy−1)2=0⇒(x−y)2=2(2xy-1)2=0⇒(x-y)2=2(vô nghiệm)
Nếu2(2xy−1)2=2⇒(x−y)2=0⇒x=y2(2xy-1)2=2⇒(x-y)2=0⇒x=y
(2x2−1)2=1⇒(2x2-1)2=1⇒[2x2−1=√12x2−1=√−1[2x2−1=12x2−1=−1 ⇒[x=−1;1x=0[x=−1;1x=0
Nếu(2xy−1)2≥2⇒2=2(2xy−1)2+(x−y)2≥4(2xy-1)2≥2⇒2=2(2xy-1)2+(x-y)2≥4(vô nghiệm)
Vậy (x;y)(x;y) thỏa mãn các cặp là (0;0);(1;1);(−1;−1)(0;0);(1;1);(-1;-1)
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Over the last century, there have been many significant changes in the way we live. Obviously, it is hard to compare the life of the ancient people and the life of the people of the twenty first century because so many changes have occured. However, even the changes that have taken place over the last ten years are amazing.To start with, people were not able to travel such long distances in such short period of time. The planes were not that popular then because they used to be a very expensive means of transport. Nowadays, we have become very mobile. We have fast and comfortable cars and more and more people also travels by plane. Moreover, in the past people had to work much harder as they did not have tools which made their work easier. Today, most of the difficult and dangerous work is done by computers and other machines. In the past the conditions of living were not as comfortable as they are now. There were not bathrooms and running water in many houses, besides many people could not afford household appliances fridge, TV set or vacuum cleaner because they used to be luxurious goods. Another difference between living now and in the past is the fact that nowadays the access to education is much easier. In the past, there were fewer schools and the quality of the education they provided was much poorer. Besides, nowadays it is much easier to find the educational materials that you need thanks to the Internet. Another difference is that in the past there were not that many sources of entertainment. Therefore people used to spend more time with their friends.All things considering, it is an obvious conclusion that life has changed significantly in the last couple of years. It is definitely much easier now however, it is not easy to decide whether it is also better. The scientific achievements and technological progress are amazing. We still create new inventions which simplify our lives. On the other hand, however, life now is much faster and more busy than it used to be in the past. Moreover, it has also become more dangerous. The standard of living has definitely improved but it can be discussed whether the quality of our lives is also better.
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https://h.vn/hoi-dap/tim-kiem?q=H%C3%B2a+tan+4,54g+h%E1%BB%97n+h%E1%BB%A3p+Al,+Fe,+Cu+trong+dung+d%E1%BB%8Bch+HCl+d%C6%B0,+thu+%C4%91%C6%B0%E1%BB%A3c+1,792+l%C3%ADt+H2H2H_2(%C4%91ktc)+v%C3%A0+1,2g+kim+lo%E1%BA%A1i.+T%C3%ADnh+ph%E1%BA%A7n+tr%C4%83m+kh%E1%BB%91i+l%C6%B0%E1%BB%A3ng+m%E1%BB%97i+kim+lo%E1%BA%A1i+trong+h%E1%BB%97n+h%E1%BB%A3p+ban+%C4%91%E1%BA%A7u&id=689446
nhận xét Cu không tác dụng với HCl -> khí H2 sinh ra là do Fe và Al phản ứng vs HCl và 1,2 g kim loại của Cu
=> m Al + Fe = 4,54-1,2=3,34 g
n H2 = 1,792:22,4=0,08 mol
Gọi n cảu Al và Fe lần lượt là x và y
\(2Al+6HCl->2AlCl_3+3H_2\)
x...................................................................1,5x
\(Fe+2HCl->FeCl_2+H_2\)
y..................................................................y
ta có m Al + Fe = 27x + 56y =3,34 g
ta lại có n H2 = 1,5x+y=0,08 mol
=> x=0,02, y=0,05
m Al = 0,02.27=0,54 g
% Cu = \(\frac{1,2}{4,54}.100\%\approx26,43\%\)
% Al = \(\frac{0,54}{4,54}.100\%\approx11,89\%\)
% Fe = 100% - 26,43%-11,89% \(\approx\) 61,69%
Dưạ vào dạng này
Bài toán tám quân hậu là bài toán đặt tám quân hậu trên bàn cờ vua kích thước 8×8 sao cho không có quân hậu nào có thể "ăn" được quân hậu khác, hay nói khác đi không quân hậu nào có để di chuyển theo quy tắc cờ vua. Màu của các quân hậu không có ý nghĩa trong bài toán này. Như vậy, lời giải của bài toán là một cách xếp tám quân hậu trên bàn cờ sao cho không có hai quân nào đứng trên cùng hàng, hoặc cùng cột hoặc cùng đường chéo. Bài toán tám quân hậu có thể tổng quát hóa thành bài toán đặt n quân hậu trên bàn cờ n×n(n ≥ 4).