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Ta có : \(3n-1⋮n-1\)
\(\Leftrightarrow3n-3+2⋮n-1\)
\(\Leftrightarrow3.\left(n-1\right)+2⋮n-1\)
\(\Leftrightarrow2⋮n-1\)
\(\Leftrightarrow n-1\inƯ\left(2\right)\)
Mà \(Ư\left(2\right)=\left\{1;-1;2;-2\right\}\)
\(\Rightarrow n-1\in\left\{1;-1;2;-2\right\}\)
\(\Rightarrow n\in\left\{2;0;3;-1\right\}\)
Vậy \(n\in\left\{2;0;3;-1\right\}\)
Chúc bạn học giỏi !!! Tham khảo cách của mk nha !!!
Áp dụng bđt AM-GM ta có:
\(\frac{x^2}{y+z}+\frac{y+z}{4}\ge2\sqrt{\frac{x^2}{y+z}.\frac{y+z}{4}}=x\)
\(\frac{y^2}{x+z}+\frac{x+z}{4}\ge2\sqrt{\frac{y^2}{x+z}.\frac{x+z}{4}}=y\)
\(\frac{z^2}{y+x}+\frac{y+x}{4}\ge2\sqrt{\frac{z^2}{y+x}.\frac{y+x}{4}}=z\)
Cộng các vế của các bđt trên ta được:
\(P+\frac{x+y+z}{2}\ge x+y+z\)
\(\Rightarrow P\ge\frac{x+y+z}{2}=1\)
Dấu"="Xảy ra \(\Leftrightarrow x=y=z=\frac{2}{3}\)
Áp dụng Svac - xơ:
\(P\ge\frac{\left(x+y+z\right)^2}{2\left(x+y+z\right)}=\frac{2^2}{2.2}=1\)
(Dấu "="\(\Leftrightarrow x=y=z=\frac{2}{3}\))
Lần sau đặt đúng môn nhé :D
Ta có: \(ab=1\Leftrightarrow b=\frac{1}{a}\)
Theo đề:
\(\frac{1}{a}+\frac{1}{b}+\frac{2}{a+b}=\frac{1}{a}+\frac{1}{\frac{1}{a}}+\frac{2}{a+\frac{1}{a}}=\frac{1}{a}+a+\frac{2}{a+\frac{1}{a}}\)
Áp dụng BĐT AM-GM:
\(\Rightarrow\frac{1}{a}+a\ge2\sqrt{1}=2\left(1\right)\Leftrightarrow\frac{2}{a+\frac{1}{a}}\ge\frac{2}{2}=1\left(2\right)\)
Cộng theo vế `(1)` và `(2)`
\(\Rightarrow\frac{1}{a}+a+\frac{2}{a+\frac{1}{a}}\ge2+1=3\)
\(\Leftrightarrow\frac{1}{a}+\frac{1}{b}+\frac{2}{a+b}\ge3\)
1, I visit you because you don't live so far away
→→If you lived so far away, i wouldn't visit you
2, You slept under a mosquito, so you weren't bitten so often
→→If you hadn't slept under a mosquito, you would have been bitten so often
3, I can get a job easily because I have a degree
→→If i didn't have a degree, i couldn't get a job easily
4, We have much rain, so our crops grow fast
→→If we diđn't have much rain, our crops wouldn't grow fast
5, We saved his life because we found him early
→→If we hadn't found him early, we wouldn't have saved his life
6, He can be a medical student because he try hard
→→If he didn't try hard, he couldn't be a medical student
ai nhanh tay tôi cho 4
Vì A=\(\frac{12}{3n-1}\)\(\Rightarrow12⋮3n-1\Rightarrow3n-1\)là Ư(12)
Mà Ư(12) ={1;-1;2;-2;3;-3;4;-4;6;-6;12;-12}
Ta lập bảng
vậy n\(\in\){0;1;-1}
chúc bạn học tốt nha !