\(\dfrac{x}{y}=\dfrac{5}{4}\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}\\ \left(\dfrac{x}{5}\right)^2=\left(\dfrac{y}{4}\right)^2\\ \dfrac{x^2}{25}=\dfrac{y^2}{16}\\ \dfrac{2x^2}{50}=\dfrac{3y^2}{48}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{2x^2}{50}=\dfrac{3y^2}{48}=\dfrac{2x^2-3y^2}{50-48}=\dfrac{288}{2}=144\\ \dfrac{2x^2}{50}=144\Rightarrow2x^2=144\cdot50=7200\Rightarrow x^2=7200:2=3600\Rightarrow x=60\\ \dfrac{3y^2}{48}=144\Rightarrow3y^2=144\cdot48=6912\Rightarrow y^2=6912:3=2304\Rightarrow y=48\\ \)
Vậy x = 60; y = 48
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