c,  Ap dung cong thuc sau  

Dien h tam giac deu canh a = \(\frac{a^2\sqrt{3}}{4}\) (bn tu chung minh )

sau do tinh canh tam giac ABC theo R se duoc \(AB=\frac{\sqrt{3}}{2}R\) thay vao cong thuc tren la ra 

d, ban tu ve hinh nha

Ta co tu giac CHMF,MHIB noi tiep 

nen suy ra \(\widehat{CHF}=\widehat{CMF},\widehat{BHI}=\widehat{BMI}\) (1)

ma \(\widehat{MCF}=\widehat{MBI}\) (tu giac ABMC noi tiep) 

=> \(\widehat{CMF}=\widehat{BMI}\) phu 2 goc bang nhau (2)

tu (1),(2) => \(\widehat{CHF}=\widehat{BHI}\) => H,I,F thang hang

khó thế =((((

Câu 3 :

\(ĐKXĐ:x>0\)

 \(P=\left(\frac{2}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+2}\right):\frac{2\sqrt{x}}{x+2\sqrt{x}}\)

\(\Leftrightarrow P=\frac{2\sqrt{x}+4+x}{x+2\sqrt{x}}\cdot\frac{x+2\sqrt{x}}{2\sqrt{x}}\)

\(\Leftrightarrow P=\frac{2\sqrt{x}+4+x}{2\sqrt{x}}\)

b) Để P = 3

\(\Leftrightarrow\frac{2\sqrt{x}+4+x}{x+2\sqrt{x}}=3\)

\(\Leftrightarrow2\sqrt{x}+4+x=6\sqrt{x}\)

\(\Leftrightarrow x-4\sqrt{x}+4=0\)

\(\Leftrightarrow\left(\sqrt{x}-2\right)^2=0\)

\(\Leftrightarrow\sqrt{x}-2=0\)

\(\Leftrightarrow\sqrt{x}=2\)

\(\Leftrightarrow x=4\)(tm)

Vậy để \(P=3\Leftrightarrow x=4\)

Câu 1 : Hình như sai đề !! Mik sửa :

\(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne4\end{cases}}\)

\(A=\left(\frac{x}{x\sqrt{x}-4\sqrt{x}}-\frac{6}{3\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\frac{10-x}{\sqrt{x}+2}\right)\)

\(\Leftrightarrow A=\left(\frac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\right):\left(\frac{x-4+10-x}{\sqrt{x}+2}\right)\)

\(\Leftrightarrow A=\frac{\sqrt{x}-2\sqrt{x}-4+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\frac{6}{\sqrt{x}+2}\)

\(\Leftrightarrow A=\frac{-6\left(\sqrt{x}+2\right)}{6\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(\Leftrightarrow A=-\frac{1}{\sqrt{x}-2}\)

b) Để A < 2

\(\Leftrightarrow-\frac{1}{\sqrt{x}-2}< 2\)

\(\Leftrightarrow-1< 2\sqrt{x}-4\)

\(\Leftrightarrow2\sqrt{x}>3\)

\(\Leftrightarrow\sqrt{x}>1,5\)

\(\Leftrightarrow x>2,25\)

Vậy để \(A< 2\Leftrightarrow x>2,25\)

-2 -1 0 1 2 3 4 1 2 3 -1 -2 (0,2) (1,0) H/ả chỉ mang t/c m.họa

a, Khi \(m=-1\Rightarrow y=-2x+2\)

b, Ta có: \(d ∩ Ox\) \(=A\left(-\frac{2}{m-1},0\right),\) \(d∩Oy=B(0,2)\)

Để \(\Delta OAB\) vuông cân:

\(\Rightarrow OA=OB\Rightarrow|-\frac{2}{m-1}|=|2|\)

\(\Rightarrow|\frac{2}{m-1}|=2\)

\(\Rightarrow|m-1|=1\)

\(\Rightarrow m-1=1\)

\(\Rightarrow m=2\)

Hoặc: \(m-1=-1\)

\(\Rightarrow m=0\)

<=> x-3=\(\sqrt{4x+9}\) 

<=>\(\left(x-3\right)^2=\sqrt{4x+9}^2\) (ĐK x>=3)

<=>x^2 - 6x +9 = 4x + 9 

<=> x^2 -10x =0

<=> x(x-10)=0

<=> x=0( ko tm ĐK) hoăc x=10 (tm)

Vây x=10 

HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEHEEEEEEEE

Nowaday, technology is developed and becomes more popular so some people use this to give us the wrong information or in another way is unreal information ; UFOs are real or ailiens are coming to our planet. We have already known that those information are untrue but some people think that those people, who give us wrong information, are telling the truth and try to make the other believe in UFOs them. However, I don't believe it. First of all, nobody have seen UFOs directly before. They just post a picture on Facebook or Instagram and say that is a real UFO. We also know that people can do everything with technology and making a fake picture of UFO is not really difficult for them. Secondly, I just believe in what scientists say or demonstrate since they just show us something just after reseaching carefully. While those people, who say that they have seen a UFO, just have an unclear picture to show us. It's so silly and stupid for some people who believe in UFOs. I think that you shouldn't believe in somethink that is unproven and just believe in what scientists or intellectuals say, not someone who want to have views and s.

   CHÚC ANH/CHỊ HỌC TỐT NHA!

Dear Mr. President,

I am writing to you about the problem of fish catching in the lake behind my house.

These days, there have been a lot of people coming here to catch the fish. The problem is that they use electricity to catch fish. This way, I think, is very dangerous. Right now, if you come here, you realize a lot of fish, small or big, are floating on the surface of the lake. Not only fish but even some other animals such as frogs, toads, and small birds are killed by electric shock waves as well.

I would suggest that you should prohibit people from catching fish here. If not, I am afraid all of the fish in the lake are not going to exist in the near future.

I look forward to seeing your resolution to this important matter.

Yours sincerely,

Nguyen Minh Phuong

Hok tốt !