mn giúp mình bài này với ạ! mình cảm ơn mn nhìu ạ:>
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1. Turn on (please+Vo)
2. Turned / off (was chia qk)
3. Look for
4. Got up (because S+ had+V3/ed, S+V2/ed)
5. Ran into( hai hd lien tiep)
6. Goes on (after S+V2/ed, S+Vht)

Bài 2: Để hệ có nghiệm duy nhất thì \(\frac{1}{a}<>\frac{a}{1}\)
=>\(a^2<>1\)
=>a∉{1;-1](1)
\(\begin{cases}ax+y=3a\\ x+ay=2a+1\end{cases}\Rightarrow\begin{cases}y=3a-ax\\ x+a\left(3a-ax\right)=2a+1\end{cases}\)
=>\(\begin{cases}y=3a-a\cdot x\\ x+3a^2-a^2\cdot x=2a+1\end{cases}\Rightarrow\begin{cases}y=3a-ax\\ x\left(1-a^2\right)=2a+1-3a^2\end{cases}\)
=>\(\begin{cases}x=\frac{-3a^2+2a+1}{1-a^2}=\frac{3a^2-2a-1}{a^2-1}=\frac{\left(a-1\right)\left(3a+1\right)}{\left(a-1\right)\left(a+1\right)}=\frac{3a+1}{a+1}\\ y=3a-a\cdot\frac{3a+1}{a+1}=\frac{3a^2+3a-3a^2-a}{a+1}=\frac{2a}{a+1}\end{cases}\)
Để x,y nguyên thì \(\begin{cases}3a+1\vdots a+1\\ 2a\vdots a+1\end{cases}\Rightarrow\begin{cases}3a+3-2\vdots a+1\\ 2a+2-2\vdots a+1\end{cases}\)
=>-2⋮a+1
=>a+1∈{1;-1;2;-2}
=>a∈{0;-2;1;-3}
Kết hợp (1), ta có: a∈{0;-2;-3}
Bài 3:
ĐKXĐ: x>=y
\(\begin{cases}\sqrt{\frac{x+y}{2}}+\sqrt{\frac{x-y}{3}}=14\\ \sqrt{\frac{x+y}{8}}-\sqrt{\frac{x-y}{12}}=3\end{cases}\Rightarrow\begin{cases}\sqrt{\frac{x+y}{2}}+\sqrt{\frac{x-y}{3}}=14\\ \frac12\left(\sqrt{\frac{x+y}{2}}-\sqrt{\frac{x-y}{3}}\right)=3\end{cases}\)
=>\(\begin{cases}\sqrt{\frac{x+y}{2}}+\sqrt{\frac{x-y}{3}}=14\\ \sqrt{\frac{x+y}{2}}-\sqrt{\frac{x-y}{3}}=6\end{cases}\Rightarrow\begin{cases}\sqrt{\frac{x+y}{2}}=10\\ \sqrt{\frac{x-y}{3}}=4\end{cases}\)
=>\(\begin{cases}\frac{x+y}{2}=100\\ \frac{x-y}{3}=16\end{cases}\Rightarrow\begin{cases}x+y=200\\ x-y=48\end{cases}\Rightarrow\begin{cases}x=\frac{200+48}{2}=\frac{248}{2}=124\\ y=200-124=76\end{cases}\) (nhận)

c)\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)....\left(1+\dfrac{1}{2020}\right)\left(1+\dfrac{1}{2021}\right)\)
\(=\left(\dfrac{1.2}{1.2}+\dfrac{1}{2}\right)\left(\dfrac{1.3}{1.3}+\dfrac{1}{3}\right)...\left(\dfrac{1.2021}{1.2021}+\dfrac{1}{2021}\right)\)
\(=\dfrac{3}{1.2}\cdot\dfrac{4}{1.3}\cdot\cdot\cdot\cdot\dfrac{2022}{1.2021}\)
\(=\dfrac{3.4.5...2022}{\left(1.1.1....1\right)\left(2.3.4...2021\right)}\)
\(=\)\(\dfrac{3.4.5...2022}{2.3.4...2021}\)
\(=\dfrac{2022}{2}=1011\)
\(d\))\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)....\left(1-\dfrac{1}{199}\right)\left(1-\dfrac{1}{200}\right)\)
\(=\left(\dfrac{2}{1.2}-\dfrac{1}{1.2}\right)\left(\dfrac{3}{1.3}-\dfrac{1}{1.3}\right)....\left(\dfrac{200}{1.200}-\dfrac{1}{1.200}\right)\)
\(=\dfrac{1.2.3....199}{\left(1.1.1....1\right).\left(2.3.4....200\right)}\)
\(=\dfrac{1.2.3...199}{2.3.4...200}\)
Nếu mik làm sai mong bạn thông cảm

a: Xét tứ giác AOBM có
góc OAM+góc OBM=180 độ
=>AOBM nội tiếp
b: \(cosAOM=\dfrac{OA}{OM}=\dfrac{1}{3}\)
nên \(\widehat{AOM}\simeq71^0\)
=>\(\widehat{AOB}\simeq142^0\)
=>sđ cung nhỏ AB là 142 độ; sđ cung lơn AB=360-142=218 độ
c:
Xét (O) có
ΔBAC nội tiếp
BC là đường kính
=>ΔBAC vuông tại A
=>BA vuông góc AC
Xét(O) có
MA,MB là tiêp tuyến
nên MA=MB
mà OA=OB
nên OM là trung trực của AB
=>OM//AC
góc ACB=góc OAC
góc OAC=góc AOM
=>góc ACB=góc AOM=góc BOM
d: góc DOM+góc BOM=90 độ
góc DMO+góc AOM=90 độ
mà góc BOM=góc AOM
nên góc DOM=góc DMO
=>DO=DM

\(\Leftrightarrow\sqrt{\left(x-2\right)^2}=7\)
\(\Leftrightarrow\left|x-2\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=7\\x-2=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-5\end{matrix}\right.\)
Ta có: \(\sqrt{x^2-4x+4}-5=2\)
\(\Leftrightarrow\left|x-2\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=7\\x-2=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-5\end{matrix}\right.\)


a)
\(=\left(\dfrac{x}{x+3}-\dfrac{x^2+9}{\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{3x+1}{x\left(x-3\right)}-\dfrac{1}{x}\right)\)
\(=\left(\dfrac{x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{x^2+9}{\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{3x+1}{x\left(x-3\right)}-\dfrac{x-3}{x\left(x-3\right)}\right)\)
\(=\left(\dfrac{x^2-3x-x^2-9}{\left(x+3\right)\left(x-3\right)}\right):\left(\dfrac{3x+1-x+3}{x\left(x-3\right)}\right)\)
\(=\dfrac{-3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}:\dfrac{2x+4}{x\left(x-3\right)}\)
\(=\dfrac{-3}{\left(x-3\right)}\cdot\dfrac{x\left(x-3\right)}{2x+4}\\ =\dfrac{-3x}{2x+4}\)
b)
với `x=-1/2` (tmđk) ta có
\(\dfrac{-3\cdot\left(\dfrac{-1}{2}\right)}{2\cdot\left(-\dfrac{1}{2}\right)+4}=\dfrac{1}{2}\)
c)
để P=x thì
\(\dfrac{-3x}{2x+4}=x\)
\(=>-3x=\left(2x+4\right)\cdot x\)
\(-3x=2x^2+4x\)
\(2x^2+4x+3x=0\)
\(2x^2+7x=0\)
\(x\left(2x+7\right)=0\)
\(=>\left[{}\begin{matrix}x=0\\2x+7=0\end{matrix}\right.=>\left[{}\begin{matrix}x=0\left(loại\right)\\x=-\dfrac{7}{2}\left(tm\right)\end{matrix}\right.\)
d)
mik ko bt lm=)
