x=2

y=4

Các bạn giải chi tiết ra cho mình nhé!

Có \(xy=\frac{x}{y}\Rightarrow y=\frac{1}{y}\Rightarrow y^2=1\Rightarrow y=\pm1\)

Với \(y=1\Rightarrow x+1=x\)(vô lý)

Với \(y=-1\Rightarrow x-1=-x\)

\(\Rightarrow2x=1\Rightarrow x=\frac{1}{2}\)

Vậy \(y=-1;x=\frac{1}{2}\)

Tham khảo nhé~

ta có \(\frac{x\left(x.y\right)}{y\left(x.y\right)}=\frac{3}{10}:\left(-\frac{3}{50}\right)=-5=\frac{x}{y}\)

\(x=-5y\)suy ra \(-5\left(-5y-y\right)=\frac{3}{10}\)suy ra \(30y^2=\frac{3}{10}\)

nên \(y=\frac{1}{10}\)hoặc \(y=-\frac{1}{10}\)

+) Với \(y=\frac{1}{10}\)suy ra \(x=-5.\frac{1}{10}=-\frac{1}{2}\)

+) Với \(y=-\frac{1}{10}\)suy ra \(x=-5.\left(-\frac{1}{10}\right)=\frac{1}{2}\).

Chúc làm bài may mắn

Từ\(x\cdot y=\frac{x}{y}\)\(\Rightarrow y^2=\frac{x}{x}=1\)\(\Rightarrow y=1,y=-1\)

Mặt khác:Từ\(x-y=x\cdot y\Rightarrow\frac{x-y}{xy}=1\Rightarrow\frac{1}{y}-\frac{1}{x}=1\)

+)  y=1=>\(1-\frac{1}{x}=1\Rightarrow0=\frac{1}{x}\)(VL)

+)  y=-1=>\(-1-\frac{1}{x}=1\Rightarrow-2=\frac{1}{x}\Rightarrow x=-\frac{1}{2}\)

Vậy.........................

Bài 1: \(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{9}=\frac{y}{12};\frac{y}{3}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{20}\)

=>\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}=\frac{2z}{18}=\frac{3y}{36}\)

Áp dụng tính chất của dãy tỉ số bằng nhau: \(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}=\frac{2z}{18}=\frac{3y}{36}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)

=>x=27;z=36;z=60

Bài 2: \(\frac{x}{2}=\frac{y}{5}=k\Rightarrow\hept{\begin{cases}x=2k\\y=5k\end{cases}}\Rightarrow xy=2k.5k=10k^2=40\Rightarrow k^2=4\Rightarrow\hept{\begin{cases}k=-2\\k=2\end{cases}}\)

+)k=-2 => x=-4;y=-5

+)k=2 => x=4;y=5

Vậy x=-4;y=-5 hoặc x=4;y=5

a,\(\frac{x}{9}=\frac{y}{12}=\frac{z}{20}\Leftrightarrow\frac{2x}{18}=\frac{3y}{36}=\frac{z}{20}=\frac{2x-3y+z}{18-36+20}=\frac{6}{2}=3\)=3  

Nhưng lâu lâu mk ms lên máy tính bàn ms gõ chữ đc thôi, còn h mk onl=ipad nên chụp hình gửi trả lời, thế mà cx bị cấm???

Từ \(x+y=1\Rightarrow x=1-y\) 

                           \(\Rightarrow y=1-x\)

Biến đổi \(\frac{y}{x^3-1}=\frac{y}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{\left(1-x\right)}{\left(x-1\right)\left(x^2+x+1\right)}=-\frac{\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=-\frac{1}{x^2+x+1}\)

            \(\frac{x}{y^3-1}=\frac{x}{\left(y-1\right)\left(y^2+y+1\right)}=\frac{\left(1-y\right)}{\left(y-1\right)\left(y^2+y+1\right)}=-\frac{\left(y-1\right)}{\left(y-1\right)\left(y^2+y+1\right)}=-\frac{1}{y^2+y+1}\)

Ta có \(\frac{y}{x^3-1}-\frac{x}{y^3-1}=\frac{-1}{x^2+x+1}-\frac{-1}{y^2+y+1}=\frac{-y^2-y-1+x^2+x+1}{\left(x^2+x+1\right)\left(y^2+y+1\right)}\)

\(=\frac{\left(x^2-y^2\right)+\left(x-y\right)}{\left(x^2+x+1\right)\left(y^2+y+1\right)}=\frac{\left(x-y\right)\left(x+y\right)+\left(x-y\right)}{\left(x^2+x+1\right)\left(y^2+y+1\right)}=\frac{\left(x-y\right)\left(x+y+1\right)}{\left(x^2+x+1\right)\left(y^2+y+1\right)}\)

\(=\frac{\left(x-y\right)\left(1+1\right)}{x^2y^2+xy^2+y^2+xy+y+x^2+x+1}\)

\(=\frac{2\left(x-y\right)}{\left(x^2y^2+x+y+1\right)+\left(x^2+y^2\right)+\left(x^2y+xy^2+xy\right)}\)

\(=\frac{2\left(x-y\right)}{\left(x^2y^2+2\right)+\left(x^2+y^2\right)+xy\left(x+y+1\right)}\)

\(=\frac{2\left(x-y\right)}{\left(x^2y^2+2\right)+\left(x^2+y^2\right)+xy\left(1+1\right)}\)

\(=\frac{2\left(x-y\right)}{\left(x^2y^2+2\right)+x^2+y^2+2xy}\)

\(=\frac{2\left(x-y\right)}{\left(x^2y^2+2\right)+\left(x+y\right)^2}\)

\(=\frac{2\left(x-y\right)}{x^2y^2+2+1}\)

\(=\frac{2\left(x-y\right)}{x^2y^2+3}\)

Vậy \(\frac{x}{y^3-1}-\frac{y}{x^3-1}=\frac{2\left(x-y\right)}{x^2y^2+3}\) với \(x+y=1\&xy\ne0\)