\(a,2^x+2^{x+3}=144\\ 2^x.\left(1+2^3\right)=144\\ 2^x.9=144\\ 2^x=144:9\\ 2^x=16=2^4\\ vậy:x=4\)

\(b,\left(x-5\right)^{2022}=\left(x-5\right)^{2021}\\ Vì:\left[{}\begin{matrix}0^{2022}=0^{2021}\\1^{2022}=1^{2021}\end{matrix}\right.\\ Vậy:\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

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

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

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

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

a) \(5\left(x+3\right)-2x\left(3+x\right)=0\\ \Leftrightarrow\left(x+3\right)\left(5-2x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\5-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{5}{2}\end{matrix}\right.\)

b) \(4x\left(x-2021\right)-x+2021=0\\ \Leftrightarrow4x\left(x-2021\right)-\left(x-2021\right)=0\\ \Leftrightarrow\left(4x-1\right)\left(x-2021\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}4x-1=0\\x-2021=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=2021\end{matrix}\right.\)

Bạn tự kết luận cả 2 câu giúp mình nhé.

a: \(5\left(x+3\right)-2x\left(x+3\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(5-2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{5}{2}\end{matrix}\right.\)

b: Ta có: \(4x\left(x-2021\right)-x+2021=0\)

\(\Leftrightarrow\left(x-2021\right)\left(4x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2021\\x=\dfrac{1}{4}\end{matrix}\right.\)

a) \(x\left(x+2021\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+2021=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-2021\end{cases}}\).

b) \(\left(x-2020\right)\left(x+2021\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2020=0\\x+2021=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2020\\x=-2021\end{cases}}\).

c) \(\left(x-2021\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2021=0\\x^2+1=0\end{cases}}\Leftrightarrow x=2021\).

d) \(\left(x+1\right)+\left(x+3\right)+\left(x+5\right)+...+\left(x+99\right)=0\)

Xét tổng: \(A=1+3+5+...+99\)

Số số hạng của dãy số là: \(\frac{99-1}{2}+1=50\).

Tổng của dãy là: \(A=\left(99+1\right)\times50\div2=2500\).

\(\left(x+1\right)+\left(x+3\right)+\left(x+5\right)+...+\left(x+99\right)=0\)

\(\Leftrightarrow50x+2500=0\)

\(\Leftrightarrow x=-50\).

Dễ thấy A chia hết cho 10 nên A có tận cùng là 0

còn 1x 3 x 5 x... x 2021 là một số lẻ và chia hết cho 5 nên có tận cùng là 5

\(a,\Leftrightarrow6x-9+4-2x=-3\Leftrightarrow4x=2\Leftrightarrow x=\dfrac{1}{2}\\ b,\Leftrightarrow\left(x-2021\right)\left(x-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2021\\x=6\end{matrix}\right.\\ c,\Leftrightarrow\left(2x-3-6x\right)\left(2x-3+6x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}-3-4x=0\\8x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=\dfrac{3}{8}\end{matrix}\right.\)

B

a)

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

P(x) + O(x) = \(3x^3-x^2+x+4041\)

b)

P(x) - O(x) = \(x^3+2x^2-3x+2020-2x^3+3x^2-4x-2021\)

P(x) - O(x) = \(-x^3+5x^2-7x-1\)