Question

Tìm \(x,y\) biết: \(x\left(x-y\right)=\dfrac{3}{10}\) và \(y\left(x-y\right)=-\dfrac{3}{50}\)

Answer 1

Ta có: \(\left(x-y\right)\left(x-y\right)=\dfrac{3}{10}+\dfrac{3}{50}\)

\(\Rightarrow\left(x-y\right)^2=\dfrac{9}{25}\)

\(\Rightarrow x-y=\pm\dfrac{3}{5}\)

+) \(x-y=\dfrac{3}{5}\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{5}x=\dfrac{3}{10}\\\dfrac{3}{5}y=\dfrac{-3}{50}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{-1}{10}\end{matrix}\right.\)

+) \(x-y=\dfrac{-3}{5}\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-1}{2}\\y=\dfrac{1}{10}\end{matrix}\right.\)

Vậy cặp số \(\left(x;y\right)\) là \(\left(\dfrac{1}{2};\dfrac{-1}{10}\right);\left(\dfrac{-1}{2};\dfrac{1}{10}\right)\)