\(B=\left(1-\frac{z}{x}\right)\left(1-\frac{x}{y}\right)\left(1-\frac{y}{z}\right)\)

\(=\left(\frac{x-z}{x}\right)\left(\frac{y-x}{y}\right)\left(\frac{z-y}{z}\right)\)

\(=\frac{x^2-y^2-z^2}{xyz}\)

Mà: x²-y²-z²=0 và xyz \(\ne\)0

\(\Rightarrow\)B=0

Mk cx k chắc nữa, sai đừng trách nha.

\(\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{2019.2020}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..-\frac{1}{2020}=1-\frac{1}{2020}=\frac{2019}{2020}\) 

\(\Rightarrow a=\frac{2020}{2019}\)

=.> 1-1/2+1/2-1/3+.......+1/2019-1/2020=1/x

=>1-1/2020=1/x

=>2019/2020=1/x

=>2019x=2020

=>x=2020/2019

    k nha

 giúp mk lên 300sp

ax = by = cz = \(\frac{x}{\frac{1}{a}}=\frac{y}{\frac{1}{b}}=\frac{z}{\frac{1}{c}}=k\left(a,b,c\ne0\right)\)

\(\Rightarrow\hept{\begin{cases}x=\frac{k}{a}\\y=\frac{k}{b}\\z=\frac{k}{c}\end{cases}\Rightarrow xyz=\frac{k^3}{abc}=\frac{8}{abc}\Rightarrow k^3=8\Rightarrow k=2\Rightarrow\hept{\begin{cases}x=\frac{2}{a}\\y=\frac{2}{b}\\z=\frac{2}{c}\end{cases}}}\)

Bài 32: 

a) P=  \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

      =   \(\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(\sqrt{4}+\sqrt{6}+\sqrt{8}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

      =   \(\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

       =   \(\frac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(1+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

        =  \(1+\sqrt{2}\)

b) Có:  \(x^2-2y^2=xy\)

\(\Leftrightarrow x^2-y^2-y^2-xy=0\)

\(\Leftrightarrow\left(x-y\right)\left(x+y\right)-y\left(y+x\right)\)

\(\Leftrightarrow\left(x+y\right)\left(x-y-y\right)=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x+y=0\\x-2y=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-y\\x=2y\end{cases}}}\)

Thay x=-y  ta có: Q=\(\frac{-y-y}{-y+y}\)=\(\frac{-2y}{0}\)(loại )

Thay x=2y ta có :   Q=\(\frac{2y-y}{2y+y}=\frac{y}{3y}=\frac{1}{3}\)