BĐT Cosi :

\(a+\dfrac{1}{a}\ge2\sqrt{a.\dfrac{1}{a}}=2\)

\(\dfrac{x-1}{9}+\dfrac{x-2}{8}+\dfrac{x-3}{7}=\dfrac{x-9}{1}+\dfrac{x-8}{2}+\dfrac{x-7}{3}\\ \Leftrightarrow\dfrac{x-1}{9}-1+\dfrac{x-2}{8}-1+\dfrac{x-3}{7}-1=\dfrac{x-9}{1}-1+\dfrac{x-8}{2}-1+\dfrac{x-7}{3}-1\\ \Leftrightarrow\dfrac{x-10}{9}+\dfrac{x-10}{8}+\dfrac{x-10}{7}=\dfrac{x-10}{1}+\dfrac{x-10}{2}+\dfrac{x-10}{3}\\ \Leftrightarrow\left(x-10\right)\left(\dfrac{1}{9}+\dfrac{1}{8}+\dfrac{1}{7}-1-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\Leftrightarrow x-10=0\\ \Leftrightarrow x=10\)

46 

tick mik nha Uzumaki Naruto

\(A=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{16}\left(1+..+16\right)\\ =1+\dfrac{1}{2}.\dfrac{\left(1+2\right).2}{2}+\dfrac{1}{3}.\dfrac{\left(1+3\right).3}{2}+....+\dfrac{1}{16}.\dfrac{\left(16+1\right).16}{2}\\ =\dfrac{2}{2}+\dfrac{\left(1+2\right)}{2}+...+\dfrac{16+1}{2}\\ =\dfrac{2+...+17}{2}\\ =\dfrac{152}{2}=76\)

\(\left(x-1\right)\left(x-2\right)>0\)

TH1:

\(\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\\ \Rightarrow x>2\)

TH2:

\(\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\\ \Rightarrow x< 1\)

Tui nop rui nhung quen mat

\(3\left(x-y\right)=7\left(y-z\right)=5\left(z-x\right)\\ \Rightarrow\dfrac{x-y}{35}=\dfrac{y-z}{15}=\dfrac{z-x}{21}\\ \)