Cái hố hả?

đúng r

giỏi quá v ta

là I

cảm ơn nhé

Ta có: \(1\cdot2\cdot3\cdot\ldots\cdot2022\)

\(=1\cdot2\cdot3\cdot\ldots\cdot7\cdot\ldots\cdot289\cdot\ldots\cdot2022\)

\(=7\cdot289\cdot1\cdot2\cdot\ldots\cdot6\cdot8\cdot\ldots\cdot288\cdot290\cdot\ldots\cdot2022\)

\(=2023\cdot1\cdot2\cdot\ldots\cdot6\cdot8\cdot\ldots\cdot288\cdot290\cdot\ldots\cdot2022\) ⋮2023

=>\(A=1\cdot2\cdot3\cdot\ldots\cdot2022\cdot\left(1+\frac12+\cdots+\frac{1}{2022}\right)\) ⋮2023

a: Ta có: \(\left(x-4\right)^2\ge0\forall x\)

=>\(A=\left(x-4\right)^2+2022\ge2022\forall x\)

Dấu '=' xảy ra khi x-4=0

=>x=4

b: Ta có: \(\left(\frac12x+\frac34\right)^{22}\ge0\forall x\)

\(\left(\frac56y-\frac78\right)^{12}\ge0\forall y\)

Do đó: \(\left(\frac12x+\frac34\right)^{22}+\left(\frac56y-\frac78\right)^{12}\ge0\forall x,y\)

=>\(\left(\frac12x+\frac34\right)^{22}+\left(\frac56y-\frac78\right)^{12}+1024\ge1024\forall x,y\)

Dấu '=' xảy ra khi \(\frac12x+\frac34=0;\frac56y-\frac78=0\)

=>\(\frac12x=-\frac34;\frac56y=\frac78\)

=>\(x=-\frac32;y=\frac78:\frac56=\frac78\cdot\frac65=\frac{42}{40}=\frac{21}{20}\)

kệ màu đỏ nhé các bạn

a: Ta có: \(A=2^{100}-2^{99}+2^{98}-2^{97}+2^{96}-\cdots+2^2-2\)

=>\(2A=2^{101}-2^{100}+2^{99}-2^{98}+\cdots+2^3-2^2\)

=>\(2A+A=2^{101}-2^{100}+2^{99}-2^{98}+\cdots+2^3-2^2+2^{100}-2^{99}+2^{98}-\cdots+2^2-2\)

=>\(3A=2^{101}-2\)

=>\(A=\frac{2^{101}-2}{3}\)

b: \(B=3^{100}-3^{99}+3^{98}-3^{97}+\cdots+3^2-3+1\)

=>\(3B=3^{101}-3^{100}+3^{99}-3^{98}+\cdots+3^3-3^2+3\)

=>\(3B+B=3^{101}-3^{100}+3^{99}-3^{98}+\cdots3^3-3^2+3+3^{100}-3^{99}+3^{98}-\cdots+3^2-3+1\)

=>\(4B=3^{101}+1\)

=>\(B=\frac{3^{101}+1}{4}\)