Question

Tìm x,y

\(\dfrac{x}{5}=\dfrac{y}{4}\)và x² - y² = 1

Answer 1

Ta có : x/5=y/4=> x=5y/4
x^2-y^2=1
=>(5y/4)^2-y^2=1
=>25y^2/16-y^2=1
=>(25y^2-16y^2)/16=1
=>9y^2=16
=>y^2=16/9
=>y=4/3
=>x=4/3 * 5/4 =5/3

Answer 2

\(\dfrac{x}{5}\) = \(\dfrac{x^2}{25}\) \(\dfrac{y}{4}=\dfrac{y^2}{16}\)

\(\dfrac{x}{5}\) = \(\dfrac{y}{4}\) \(\Rightarrow\) \(\dfrac{x^2}{25}\) = \(\dfrac{y^2}{16}\) = \(\dfrac{x^2-y^2}{25-16}\) = \(\dfrac{1}{9}\)

\(\dfrac{x}{5}\) = \(\dfrac{1}{9}\) \(\Rightarrow\) x.9 = 1.5 x \(\Rightarrow\) x.9 = 5 \(\Rightarrow\) x = 5:9 \(\Rightarrow\)x = \(\dfrac{5}{9}\)

\(\dfrac{y}{4}\) = \(\dfrac{1}{9}\) \(\Rightarrow\) y.9 = 1.4 \(\Rightarrow\) x.9 = 4 \(\Rightarrow\) x = 4:9 \(\Rightarrow\)x = \(\dfrac{4}{9}\)