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9 tháng 5 2022

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7 tháng 3 2020

Ta có : A=22+24+26+...+220

=(22+24)+(26+28)+...+(218+220)

=22(1+22)+26(1+22)+...+218(1+22)

=22.5+26.5+...+218.5 chia hết cho 5

Vậy A chia hết cho 5.

\(A=2^2+2^4+2^6..+2^{18}+2^{20}\)

\(\Leftrightarrow A=\left(2^2+2^4\right)+\left(2^6+2^8\right)+...+\left(2^{18}+2^{20}\right)\)

\(\Leftrightarrow A=20+2^4.\left(2^2+2^4\right)+...+2^{16}.\left(2^2+2^4\right)\)

\(\Leftrightarrow A=20+2^4.20+..+2^{16}.20\)

\(\Leftrightarrow A=20\left(1+2^4+..+2^{16}\right)\)

Vì \(20⋮5\)

\(\Rightarrow A=20\left(1+2^4+..+2^{16}\right)⋮5\)

Vậy \(A⋮5\)

hok tốt!!

23 tháng 12 2023

A=1+2+22+...+22009 gồm 2010 số
A=(1+2+22)+(23+24+25)+...+(22007+22008+22009)
A=7.1+7.23+...+7.22007(. là dấu nhân nhaaa)
A=7.(1+23+...+22007)
⋮7
Vậy A⋮7
tích đúng hộ mikkkkk

 

Tọa độ giao điểm A,B là nghiệm của hệ phương trình:

\(\left\{{}\begin{matrix}x^2=2x+3\\y=2x+3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)\left(x+1\right)=0\\y=2x+3\end{matrix}\right.\Leftrightarrow\left(x,y\right)\in\left\{\left(3;9\right);\left(-1;1\right)\right\}\)

vậy: A(3;9); B(-1;1)

27 tháng 10 2021

a) \(\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\mx+y=m+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\\left(m-1\right)-mx=2-\left(m+1\right)\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\-x=1-m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)^2+y=2\\x=m-1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=2-\left(m-1\right)^2\\x=m-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-m^2+2m+1\\x=m-1\end{matrix}\right.\)

\(2x+y=2\left(m-1\right)+\left(-m^2+2m+1\right)=2m-2-m^2+2m+1=-m^2+4m-1=-\left(m^2-4m+4\right)+3=-\left(m-2\right)^2+3\le3\)

Dấu "=" xảy ra \(\Leftrightarrow m=2\)

 

27 tháng 10 2021

\(a,HPT\Leftrightarrow\left\{{}\begin{matrix}mx-x+y=2\\mx+y=m+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}mx+y=x+2\\mx+y=m+1\end{matrix}\right.\\ \Leftrightarrow x+2=m+1\Leftrightarrow x=m-1\\ \Leftrightarrow\left(m-1\right)^2+y=2\\ \Leftrightarrow y=2-\left(m-1\right)^2\)

\(2x+y\le3\\ \Leftrightarrow2m-2+2-m^2+2m-1-3\le0\\ \Leftrightarrow-m^2+4m-4\le0\\ \Leftrightarrow-\left(m-2\right)^2\le0\left(luôn.đúng\right)\)

Vậy ta được đpcm

b, \(x+y=-4\Leftrightarrow x=-4-y\Leftrightarrow\left\{{}\begin{matrix}m-1=-4-y\left(1\right)\\y=2-\left(m-1\right)^2\left(2\right)\end{matrix}\right.\)

Thế (2) vào (1)

\(\Leftrightarrow m-1=-4-2+\left(m-1\right)^2\\ \Leftrightarrow m-1=-6+m^2-2m+1\\ \Leftrightarrow m^2-3m-4=0\\ \Leftrightarrow\left[{}\begin{matrix}m=-1\\m=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}y=2-4=-2\\y=2-9=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left\{\left(-2;-2\right);\left(3;-7\right)\right\}\)

25 tháng 5 2022

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25 tháng 5 2022

When a tropical storm reaches 120 kilometers per hour, it is called a typhoon

Wearing uniforms encourages students to be proud of being students of their school

the weather was snowy, we couldn't go to work yesterday
put the garbage into the dustbins, we will minimize pollution
so slowly that his students get bored
difficult to find a better solution