Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x>y\),\(xy=1\)
Ta có:
\(\frac{x^2+y^2}{x-y}=\frac{\left(x^2-2xy+y^2\right)+2xy}{x-y}=\frac{\left(x-y\right)^2+2}{x-y}=x-y+\frac{2}{x-y}\)
Áp dụng BĐT Cauchy ta có:
\(x-y+\frac{2}{x-y}\ge2\sqrt{\left(x-y\right).\frac{2}{x-y}}=2\sqrt{2}\)
\(\Rightarrow\frac{x^2+y^2}{x-y}\ge2\sqrt{2}\)(đpcm)
Chúc bạn học tốt
Environment is an essential part of our life. A clean environment is necessary for a peaceful and healthy life. An environment is the natural surroundings which helps human beings, animals and other living things to grow and develop naturally. But nowadays, our environment is disturbing in many different ways. Any type of disturbance in the nature’s balance affects the environment totally. It does not only ruin human lives but also affects on all living beings. We can save our environment with the little step taken by everyone on the earth. We should reduce the amount of waste, throwing wastes properly to its place only…and many other simple ways. It is very important to save environment for human existence. When we protect the environment, we are protecting ourselves and our future as well.
Enviroment is one of the most important things for our life. Enviroment is the air we breath, the water we drink and is everything we need for our life. But now that most important thing for our life is being polluted and by many different ways. This pollution affects the health of living things. Air is damaged by car and lorry fumes, and power stations create acid rain which destroys entire forests and lakes. When fossil fuels i.e. oil, gas and coal are burned to provide energy for lighting, cooking etc. they form polluting gases. Not only on land but also in the sea, oils spills pollute sea water and kill marine life; chemical waste from factories and sewage works, and artificial fertilisers from farmland, pollute river water, killing wildlife and spreading disease. Everything is being caused by human’s existence. Humans create such a lot of rubbish! Each household produces about 1 tonne of rubbish every year! Most of this is taken away by dustmen and buried in enormous landfill sites or burned in incinerators – both of these actions can be dangerous for the environment.
But only we can change it and solve it. Pollution can be prevented by thing we do everyday. First we can use recycled paper to help save trees. Second try to avoid buying plas. It’s hard to recycle. One way to cut down on plas is to refuse to use carrier bags. If we can’t avoid buying plas bags, we should use re-use plas bags over and over again, until they wear out. Finally we should take your old clothes to charity shops, some are sold. To protect environment we also have to save energy. Use less energy by switching off lights when rooms are not in use, not wasting water; don’t forget to switch off all electric things when they are not in use, use a bicycle or walk instead of using a car for short trips we can save energy, keep clean atmosphere and keep healthy life. Lighting accounts for 10 percent to 15 percent of the electricity bill. However, this amount can be reduced by replacing an ordinary 100-watt light bulb with an energy-saving bulb and we still trying to invent the new thing to save money as well as conserve the Earth’s resources.
Keep clean environment isn’t only all ways are mentioned before but also to protect natural resources. That is the way to conserver wild life. First we need to conserve the old forest, rainforest, build more safari and national park, and plant more trees to make place to live for wild animals. Second we need to prohibit hunters who hunt animals too many out of the law allowance.
Finally, we now know that enviroment plays an important role in our life life and we know how to protect and use it scientifically. Everyday we invent and find more and more way to protect enviroment. I hope that in the future the earth will be cleaner and more beautiful!
\(ĐKXĐ:x\ge\frac{5}{3}\)
\(\left(\sqrt{8x+1}-5\right)+\left(\sqrt{3x-5}-2\right)=\left(\sqrt{7x+4}-5\right)+\left(\sqrt{2x-2}-2\right)\)
\(\Leftrightarrow\frac{8x+1-25}{\sqrt{8x+1}+5}+\frac{3x-5-4}{\sqrt{3x-5}+2}-\frac{7x+4-25}{\sqrt{7x+4}+5}-\frac{2x-2-4}{\sqrt{2x-2}+2}=0\)
\(\Leftrightarrow\left(x-3\right)\left[\frac{8}{\sqrt{8x+1}+5}+\frac{3}{\sqrt{3x-5}+2}-\frac{7}{\sqrt{7x+4}+5}-\frac{2}{\sqrt{2x-2}+2}\right]=0\)
Ngoặc trong chắc vô nghiệm :3
Ta có B = 12 + 22 + 32 + ... + 982
= 1.1 + 2.2 + 3.3 + ... + 98.98
= 1.(2 - 1) + 2.(3 - 1) + 3.(4 - 1) + ... + 98.(99 - 1)
= 1.2 + 2.3 + 3.4 + ... + 98.99 - (1 + 2 + 3 + ... + 98)
= 1.2 + 2.3 + 3.4 + ... + 98.99 - 98.(98 + 1) : 2
= 1.2 + 2.3 + 3.4 + ... + 98.99 - 4851
Khi đó B - A = (1.2 + 2.3 + 3.4 + ... + 98.99 - 4851) - 1.2 + 2.3 + 3.4 + ... + 98.99
= 1.2 + 2.3 + 3.4 + ... + 98.99 - 4851 - 1.2 + 2.3 + 3.4 + ... + 98.99
= -4851
Vậy B - A = - 4851
Ta có: \(y'=a\)\(cosx-b\)\(sinx+1\)
y đồng biến trên R \(\Leftrightarrow y'\ge0,\forall x\in R\)
\(\Leftrightarrow acosx-bsinx+1\ge0,\forall x\in R\)(*)
Theo bất đẳng thức Schwartz thì:
\(|acosx-bsinx|\le\sqrt{a^2+b^2},\forall x\)
\(\Leftrightarrow-\sqrt{a^2+b^2}\le acos-bsinx\le\sqrt{a^2+b^2},\forall x\)
\(\Leftrightarrow1-\sqrt{a^2+b^2}\le acos-bsinx+1\le1+\sqrt{a^2+b^2},\forall x\)
Do đó (*) \(\Leftrightarrow1-\sqrt{a^2+b^2}\ge0\)
\(\Leftrightarrow\sqrt{a^2+b^2}\le1\)
\(\Leftrightarrow a^2+b^2\le1\)
Ta có : \(h_1=13,6h_2\)=> \(\frac{h_1}{h_2}=\frac{13,6}{1}\)hay \(\frac{h_1}{13,6}=\frac{h_2}{1}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có : \(\frac{h_1}{13,6}=\frac{h_2}{1}=\frac{h_1+h_2}{13,6+1}=\frac{0,44}{14,6}=\frac{11}{365}\)
=> \(h_1=\frac{11}{365}\cdot13,6=\frac{748}{1825}\)
\(h_2=\frac{11}{365}\cdot1=\frac{11}{365}\)
P/S : Đề như thế nào?Số dữ quá
Ta có :
\(a+b+c=0\Rightarrow b+c=-a\Rightarrow\left(b+c\right)^2=\left(-a\right)^2\)
\(\Rightarrow b^2+2bc+c^2=a^2\Rightarrow a^2-b^2-c^2=2bc\)
Tương tự \(b^2-c^2-a^2=2ca;c^2-a^2-b^2=2ab\)
Mặt khác \(\left(b+c\right)^2=\left(-a\right)^2\Rightarrow b^3+3bc\left(b+c\right)+c^3=-a^3\Rightarrow a^3+b^3+c^3=-3bc\left(b+c\right)\)
\(\Rightarrow a^3+b^3+c^3=3abc\)
\(\Rightarrow P=\frac{a^2}{a^2-b^2-c^2}+\frac{b^2}{b^2-c^2-a^2}+\frac{c^2}{c^2-a^2-b^2}=\frac{a^2}{2bc}+\frac{b^2}{2ac}+\frac{c^2}{2ba}=\frac{a^3+b^3+c^3}{2abc}\)
\(=\frac{3abc}{2abc}=\frac{3}{2}\)
Vậy P = 3/2
em mới lớp 6-7 nên em sẽ giải theo kiểu lớp 6 là
em ko biết giải khó quá trời