Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1: \(M=0\)
mà \(\left\{{}\begin{matrix}\left(x-2021\right)^{2022}>=0\\\left(2021-y\right)^{2020}>=0\end{matrix}\right.\)
nên x-2021=0 và 2021-y=0
=>x=2021 và y=2021
a) Thay \(a = - 4,b = 18\)vào đa thức ta có:
\(A = - 5a - b - 20 = - 5. - 4 - 18 - 20 = - 18\).
b) Thay \(x = - 1,y = 3,z = - 2\)vào đa thức ta có:
\(B = - 8xyz + 2xy + 16y = - 8. - 1.3. - 2 + 2. - 1.3 + 16.3 = - 48 - 6 + 48 = - 6\).
c) Thay \(x = - 2,y = - 3\)vào đa thức ta có:
\(C = - {x^{2021}}{y^2} + 9{x^{2021}} = - {( - 1)^{2021}}.{( - 3)^2} + 9.{( - 1)^{2021}} = - ( - 1).9 + 9.( - 1) = 9 + ( - 9) = 0\).
\(\dfrac{y+z+t-2020x}{x}=\dfrac{z+t+x-2020y}{y}=\dfrac{t+x+y-2020z}{z}=\dfrac{x+y+z-2020t}{t}=\dfrac{-2017\left(x+y+z+t\right)}{x+y+z+t}=-2017\\ \Leftrightarrow\left\{{}\begin{matrix}y+z+t-2020x=-2017x\\z+t+x-2020y=-2017y\\t+x+y-2020z=-2017z\\x+y+z-2020t=-2017t\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+y+z+t=2x\\x+y+z+t=2y\\x+y+z+t=2z\\x+y+z+t=2t\end{matrix}\right.\\ \Leftrightarrow x=y=z=t=\dfrac{x+y+z+t}{2}=1010\\ \Leftrightarrow A=1010\left(2019-2020+2021-2022\right)=1010\left(-2\right)=-2020\)
P = x3 - y2 + x + x2y - 2x2 + 3y - xy + 2021
= x3 - y2 + x + x2y - (x + y)x2 + 3y - xy + 2021 (do x + y = 2)
= x3 - y2 + x + x2y - x3 - x2y + 3y - xy + 2021
= -y2 + x + 3y - xy + 2021
= -y2 + 2y - xy + (x + y) + 2021
= -y2 + (x + y).y - xy + 2 + 2021 (Do x + y = 2)
= -y2 + xy + y2 - xy + 2023
= 2023
Vậy P = 2023
A(1/2^2022)=1/2^2022+1/2^4044+...+1/2^(2022^2021)
=>2^2022*A=1+1/2^2022+...+1/2^(2022^2020)
=>A*(2^2022-1)=1-1/2^(2022^2021)
=>\(A=\dfrac{2^{2022^{2021}}-1}{2^{2022}-1}\)
Ta có:
\(\frac{x}{2}=\frac{y}{3}=k\Rightarrow\left\{{}\begin{matrix}x=2k\\y=3k\end{matrix}\right.\)
\(\Rightarrow A=\frac{2019x+2020y}{2019x-2020y}=\frac{2019.2k+2020.3k}{2019.2k-2020.3k}=\frac{10098k}{-2022k}=\frac{10098}{-2022}=\frac{-1683}{337}\)
Ta có:
\(\frac{x}{2}=\frac{y}{3}.\)
Đặt \(\frac{x}{2}=\frac{y}{3}=k\Rightarrow\left\{{}\begin{matrix}x=2k\\y=3k\end{matrix}\right.\)
Lại có: \(A=\frac{2019x+2020y}{2019x-2020y}.\)
+ Thay \(x=2k\) và \(y=3k\) vào A ta được:
\(A=\frac{2019.2k+2020.3k}{2019.2k-2020.3k}\)
\(\Rightarrow A=\frac{4038k+6060k}{4038k-6060k}\)
\(\Rightarrow A=\frac{k.\left(4038+6060\right)}{k.\left(4038-6060\right)}\)
\(\Rightarrow A=\frac{4038+6060}{4038-6060}\)
\(\Rightarrow A=\frac{10098}{-2022}\)
\(\Rightarrow A=\frac{-1683}{337}.\)
Vậy \(A=\frac{-1683}{337}.\)
Chúc bạn học tốt!
b: \(=1^{2020}\cdot\left(-1\right)^{2021}+4\cdot1^{2020}\cdot\left(-1\right)^{2021}-2\cdot1^{2020}\cdot\left(-1\right)^{2021}\)
\(=1\cdot\left(-1\right)+4\cdot1\cdot\left(-1\right)-2\cdot1\cdot\left(-1\right)\)
=-1-4+2
=-3