Question

Tìm x, y biết:

\(\frac{3}{5}x=\frac{2}{3}y\) và x² - y² = 38

Answer 1

3/5 x= 2/3 y ->y=9/10x

x^2 -y^2=38 -> x^2 - (9/10)^2= 38
giải pt đó để tìm x nhá :)

Answer 2

Ta có: \(\frac{3}{5}x=\frac{2}{3}y\Leftrightarrow\frac{x}{y}=\frac{\frac{2}{3}}{\frac{3}{5}}=\frac{10}{9}\Leftrightarrow\frac{x^2}{y^2}=\frac{100}{81}\Leftrightarrow81x^2=100y^2\Leftrightarrow81x^2-100y^2=0\)

\(\Leftrightarrow81\left(x^2-y^2\right)-19y^2=0\Leftrightarrow81.38=19y^2\Leftrightarrow y^2=\frac{81.38}{19}=162\Leftrightarrow y=\sqrt{162}\)

Suy ra: \(x=\frac{10}{9}y=\frac{10}{9}\sqrt{162}=\frac{10\sqrt{162}}{9}\).