Ta có: \(\dfrac{x}{y}=\dfrac{3}{5}\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}\)
Đặt \(\dfrac{x}{3}=\dfrac{y}{5}=k\)
\(\Rightarrow x=3k\)
\(y=5k\)
Khi đó \(P=\dfrac{5x^2+3y^2}{10x^2-3y^2}=\dfrac{5.\left(3k\right)^2+3.\left(5k\right)^2}{10.\left(3k\right)^2-3.\left(5k\right)^2}\)
\(=\dfrac{5.9k^2+3.25k^2}{10.9k^2-3.25k^2}=\dfrac{45k^2+75k^2}{90k^2-75k^2}\)
\(=\dfrac{120k^2}{15k^2}=\dfrac{120}{15}=8.\)
\(\dfrac{x}{y}=\dfrac{3}{5}\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}\Rightarrow x=3k;y=5k\)
\(P=\dfrac{5x^2+3y^2}{10x^2-3y^2}\)
\(P=\dfrac{5.3k^2+3.5k^2}{10.3k^2-3.5k^2}\)
\(P=\dfrac{15k^2+15k^2}{30k^2-15k^2}\)
\(P=\dfrac{30k^2}{15k^2}=2\)
