Question

Tìm x,y biết:

x.(x-y)=44/3

y.(x-y)=11/9

Answer 1

Vì x.(x-y) = 44/3 

     x.x-y=44/3

     x2-y=44/3

     x.2=44/3-y

     x2=44/3-(y+1)

x2=44/3-1

x2=41/3

x=41/3/2

x=41/6

y=44/3-44/6

y=44/6

Answer 2

Từ đầu bài suy ra:

\(x\left(x-y\right)-y\left(x-y\right)=\frac{44}{3}-\frac{11}{9}\)

\(\Rightarrow\left(x-y\right)\left(x-y\right)=\frac{132}{9}-\frac{11}{9}\)

\(\Rightarrow\left(x-y\right)^2=\frac{121}{9}\)

\(\Rightarrow\left(x-y\right)^2=\left(-\frac{11}{3}\right)^2\)hoặc \(\left(x-y\right)^2=\left(\frac{11}{3}\right)^2\)

\(\Rightarrow x-y=-\frac{11}{3}\)hoặc \(x-y=\frac{11}{3}\)

+)Nếu \(x-y=-\frac{11}{3}\)

\(\Rightarrow x=\frac{44}{3}:\left(-\frac{11}{3}\right)=\frac{44}{3}.\frac{-3}{11}=\frac{-44}{11}=-4\)và \(y=\frac{11}{9}:\left(-\frac{11}{3}\right)=\frac{11}{9}.\frac{-3}{11}=\frac{-3}{9}=\frac{-1}{3}\)

+)Nếu \(x-y=\frac{11}{3}\)

\(\Rightarrow x=\frac{44}{3}:\frac{11}{3}=\frac{44}{3}.\frac{3}{11}=\frac{44}{11}=4\)và \(y=\frac{11}{9}:\frac{11}{3}=\frac{11}{9}.\frac{3}{11}=\frac{3}{9}=\frac{1}{3}\)

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