Ta có: \(x=2021\Rightarrow2020=x-1\)

Thay vào được:

\(A=x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x\)

\(A=x^4-x^4+x^3-x^3+x^2-x^2+x\)

\(A=x=2021\)

Vậy A  = 2021

Ta có: \(x=2021\)\(\Rightarrow x-1=2020\)

Thay \(x-1=2020\)vào biểu thức A ta được:

\(A=x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x\)

\(=x^4-x^4+x^3-x^3+x^2-x^2+x\)

\(=x=2021\)

Theo bài ra ta có : \(x=2021\Leftrightarrow x-1=2020\)

hay \(A=x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x\)

\(=x^4-x^4+x^3-x^3+x^2-x^2+x=x\)

\(\Rightarrow x=2021\)Vậy biểu thức A nhận giá trị 2021 

Thay `x=2021` vào A: `A=2020.2021-2022 .2021^2 +2021^3=-2021`

x=2021⇒2020=x-1; 2022=x+1, thay vào A ta có:

A=2020x-2022x²+x³

=(x-1)x-(x+1)x²+x³

=x²-x-x³-x²+x³

=x

=2021

x=2021⇒2020=x-1; 2022=x+1, thay vào A ta có:

A=2020x-2022x²+x³

=(x-1)x-(x+1)x²+x³

=x²-x-x³-x²+x³

=-x

=-2021

a: \(A=\left(2x-5\right)^2-4x\left(x-5\right)\)

\(=4x^2-20x+25-4x^2+20x\)

=25

b: \(B=\left(4-3x\right)\left(4+3x\right)+\left(3x+1\right)^2\)

\(=16-9x^2+9x^2+6x+1\)

=6x+17

c: \(C=\left(x+1\right)^3-x\left(x^2+3x+3\right)\)

\(=x^3+3x^2+3x+1-x^3-3x^2-3x\)

=1

d: \(D=\left(2021x-2020\right)^2-2\left(2021x-2020\right)\left(2020x-2021\right)+\left(2020x-2021\right)^2\)

\(=\left(2021x-2020-2020x+2021\right)^2\)

\(=\left(x+1\right)^2\)

\(=x^2+2x+1\)

\(Q\left(x\right)=x^{101}-2020x^{100}-2022x^{99}+2022x^{98}+x-2021\)

\(=x^{100}\left(x-2021\right)+x^{99}\left(x-2021\right)-x^{98}\left(x-2021\right)+x^{98}+x-2021\)

\(Q\left(2021\right)=0+0-0+2021^{98}+0=2021^{98}\)

TK: Câu hỏi của Hà Phương Linh - Toán lớp 9 - Học trực tuyến OLM

Theo vi et: \(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=\dfrac{-2020}{1}=-2020\\x_1x_2=\dfrac{c}{a}=\dfrac{2021}{1}=2021\end{matrix}\right.\)

a

\(\dfrac{1}{x_1}+\dfrac{1}{x_2}=\dfrac{x_2}{x_1x_2}+\dfrac{x_1}{x_1x_2}=\dfrac{x_1+x_2}{x_1x_2}=\dfrac{-2020}{2021}\)

b

\(x_1^2+x_2^2=x_1^2+2x_1x_2+x_2^2-2x_1x_2=\left(x_1+x_2\right)^2-2x_1x_2=\left(-2020\right)^2-2.2021=4076358\)

Đề sai. Nếu $x,y$ đều âm thì điều kiện $xy> 2020x+2020y$ được thỏa mãn nhưng hiển nhiên $x+y$ không thể lớn hơn $(\sqrt{2020}+\sqrt{2021})^2$

\(x^5-2022x^4+2020x^3+2020x^2-2020x-2021\)

=\(x^5-x^4-2021x^4+2021x^3-x^3+x^2+2021x^2-2021x+x-1-2020\)

=\(x^4\left(x-1\right)-2021x^3\left(x-1\right)-x^2\left(x+1\right)+2021x\left(x-1\right)+\left(x-1\right)-2020\)

=\(\left(x^4-2021x^3-x^2+2021x+1\right).\left(x-1\right)-2020\)

=\(\left[x^3\left(x-2021\right)-x\left(x-2021\right)+1\right]\left(x-1\right)-2020\)

=\(\left[\left(x^3-x\right).\left(x-2021\right)+1\right]\left(x-1\right)-2020\)*

vì x-2021 luôn bằng 0 \(\Rightarrow\left[\left(x^3-x\right).0+1\right]=1\)

*=1.(2021-1)-2020=0

đây nha bạn //