cái thứ 2 em tải hình xuống đề phòng hình 1 mất ạ

Bài 1: 

1: \(\sqrt{3+2\sqrt{2}}=\sqrt{2}+1\)

2: \(\sqrt{5-2\sqrt{6}}=\sqrt{3}-\sqrt{2}\)

3: \(\sqrt{11-2\sqrt{30}}=\sqrt{6}-\sqrt{5}\)

4: \(\sqrt{7-2\sqrt{10}}=\sqrt{5}-\sqrt{2}\)

BÀi 4:

a: Xét ΔEAD và ΔECF co

EA=EC

\(\hat{AED}=\hat{CEF}\) (hai góc đối đỉnh)

ED=EF

Do đó: ΔEAD=ΔECF

b: ΔEAD=ΔECF

=>\(\hat{EAD}=\hat{ECF}\)

mà hai góc này là hai góc ở vị trí so le trong

nên AD//CF

=>DB//CF

ΔEAD=ΔECF

=>AD=CF

mà AD=DB

nên DB=CF

Xét ΔFDC và ΔBCD có

FC=BD

\(\hat{FCD}=\hat{BDC}\) (hai góc so le trong, FC//BD)

CD chung

Do đó: ΔFDC=ΔBCD

=>FD=BC

=>\(DE=\frac12DF=\frac12\cdot BC\)

BÀi 2:

\(\frac14x-\frac75=-\frac53\)

=>\(\frac14x=-\frac53+\frac75=\frac{-25+21}{15}=-\frac{4}{15}\)

=>\(x=-\frac{4}{15}\cdot4=-\frac{16}{15}\)

1) \(\sqrt{2x-5}=7\)

\(\left(\sqrt{2x-5}\right)^2=7^2\)

\(2x-5=49\)

\(2x=54\)

\(x=27\)

2) \(3+\sqrt{x-2}=4\)

\(\sqrt{x-2}=1\)

\(\left(\sqrt{x-2}\right)^2=1^2\)

\(x-2=1\)

\(x=3\)

1) \(\sqrt{2x-5}=7\left(đk:x\ge\dfrac{5}{2}\right)\)

\(\Leftrightarrow2x-5=49\Leftrightarrow2x=54\Leftrightarrow x=27\left(tm\right)\)

2) \(3+\sqrt{x-2}=4\left(đk:x\ge2\right)\)

\(\Leftrightarrow\sqrt{x-2}=1\Leftrightarrow x-2=1\Leftrightarrow x=3\)

3) \(\Leftrightarrow\sqrt{\left(x-1\right)^2}=1\Leftrightarrow\left|x-1\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

4) \(\Leftrightarrow\sqrt{\left(x-2\right)^2}=1\Leftrightarrow\left|x-2\right|=1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

5) \(\Leftrightarrow\sqrt{\left(2x-1\right)^2}=\sqrt{\left(x+4\right)^2}\)

\(\Leftrightarrow\left|2x-1\right|=\left|x+4\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=x+4\\2x-1=-x-4\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

6) \(ĐK:x\ge-2\)

 \(\Leftrightarrow5\sqrt{x+2}-3\sqrt{x+2}-\sqrt{x+2}=\sqrt{x+7}\)

\(\Leftrightarrow\sqrt{x+2}=\sqrt{x+7}\)

\(\Leftrightarrow x+2=x+7\Leftrightarrow2=7\left(VLý\right)\)

Vậy \(S=\varnothing\)

7) \(ĐK:x\ge-1\)

\(\Leftrightarrow5\sqrt{2x+1}+3\sqrt{x+1}=4\sqrt{x+1}+4\sqrt{2x+1}\)

\(\Leftrightarrow\sqrt{2x+1}=\sqrt{x+1}\)

\(\Leftrightarrow2x+1=x+1\Leftrightarrow x=0\left(tm\right)\)

nhưng câu dễ thì vẫn nên tự làm ik

làm không làm mà đi nhắc báo cáo

Bài 3:

a: \(M=\frac{x+12}{x-4}+\frac{1}{\sqrt{x}+2}-\frac{4}{\sqrt{x}-2}\)

\(=\frac{x+12+\sqrt{x}-2-4\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{x+\sqrt{x}+10-4\sqrt{x}-8}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=\frac{x-3\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-1}{\sqrt{x}+2}\)

b: Đặt \(P=\frac{1}{M}\)

\(=1:\frac{\sqrt{x}-1}{\sqrt{x}+2}=\frac{\sqrt{x}+2}{\sqrt{x}-1}\)

Để P là số nguyên thì \(\sqrt{x}+2\) ⋮\(\sqrt{x}-1\)

=>\(\sqrt{x}-1+3\) ⋮\(\sqrt{x}-1\)

=>3⋮\(\sqrt{x}-1\)

=>\(\sqrt{x}-1\in\left\lbrace1;-1;3;-3\right\rbrace\)

=>\(\sqrt{x}\in\left\lbrace2;0;4;-2\right\rbrace\)

=>\(\sqrt{x}\in\left\lbrace0;2;4\right\rbrace\)

=>x∈{0;4;16}

Kết hợp ĐKXĐ, ta được: x∈{0;16}

c: \(M-1=\frac{\sqrt{x}-1}{\sqrt{x}+2}-1=\frac{\sqrt{x}-1-\sqrt{x}-2}{\sqrt{x}+2}=\frac{-3}{\sqrt{x}+2}<0\)

=>M<1

d: \(M^2=-M\)

=>M(M+1)=0

=>M=0 hoặc M=-1

=>\(\left[\begin{array}{l}\frac{\sqrt{x}-1}{\sqrt{x}+2}=0\\ \frac{\sqrt{x}-1}{\sqrt{x}+2}=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}\sqrt{x}-1=0\\ \sqrt{x}-1=-\sqrt{x}-2\end{array}\right.\)

=>\(\left[\begin{array}{l}\sqrt{x}=1\\ 2\sqrt{x}=-1\end{array}\right.\Rightarrow\sqrt{x}=1\)

=>x=1(nhận)

Bài 4:

a: \(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\)

\(=\frac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\sqrt{x}}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}\)

\(=\frac{x+2+\sqrt{x}\left(\sqrt{x}-1\right)-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

\(=\frac{-\sqrt{x}+1+\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}-1}{x+\sqrt{x}+1}\)

Ta có: \(P=\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\right):\frac{\sqrt{x}-1}{2}\)

\(=\frac{\sqrt{x}-1}{x+\sqrt{x}+1}\cdot\frac{2}{\sqrt{x}-1}=\frac{2}{x+\sqrt{x}+1}\)

b: \(x+\sqrt{x}+1=\sqrt{x}\left(\sqrt{x}+1\right)+1>0\forall x\) thỏa mãn ĐKXĐ

2>0

Do đó: \(P=\frac{2}{x+\sqrt{x}+1}>0\forall x\) thỏa mãn ĐKXĐ

Bài 1:

1: Thay x=9 vào A, ta được:

\(A=\frac{\sqrt9+1}{\sqrt9-1}=\frac{3+1}{3-1}=\frac42=2\)

2:

a: \(\frac{x-2}{x+2\sqrt{x}}+\frac{1}{\sqrt{x}+2}\)

\(=\frac{x-2}{\sqrt{x}\left(\sqrt{x}+2\right)}+\frac{1}{\sqrt{x}+2}=\frac{x+\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}+2\right)}\)

\(=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}=\frac{\sqrt{x}-1}{\sqrt{x}}\)

Ta có: \(P=\left(\frac{x-2}{x+2\sqrt{x}}+\frac{1}{\sqrt{x}+2}\right)\cdot\frac{\sqrt{x}+1}{\sqrt{x}-1}\)

\(=\frac{\sqrt{x}-1}{\sqrt{x}}\cdot\frac{\sqrt{x}+1}{\sqrt{x}-1}=\frac{\sqrt{x}+1}{\sqrt{x}}\)

b: \(2P=2\sqrt{x}+5\)

=>\(\frac{2\sqrt{x}+2}{\sqrt{x}}=2\sqrt{x}+5\)

=>\(2x+5\sqrt{x}=2\sqrt{x}+2\)

=>\(2x+3\sqrt{x}-2=0\)

=>\(2x+4\sqrt{x}-\sqrt{x}-2=0\)

=>\(\left(\sqrt{x}+2\right)\left(2\sqrt{x}-1\right)=0\)

=>\(2\sqrt{x}-1=0\)

=>\(2\sqrt{x}=1\)

=>\(\sqrt{x}=\frac12\)

=>x=1/4(nhận)

3n + 4 = 3n - 6 + 10

= 3(n - 2) + 10

Để (3n + 4) ⋮ (n - 2) thì 10 ⋮ (n - 2)

⇒ n - 2 ∈ Ư(10) = {-10; -5; -2; -1; 1; 2; 5; 10}

⇒ n ∈ {-8; -3; 0; 1; 3; 4; 7; 12}

Mà n là số tự nhiên

⇒ n ∈ {0; 1; 3; 4; 7; 12}