a/ cách 1: x/y = 17/3
=> \(\dfrac{x}{17}=\dfrac{y}{3}\) vaf x + y = -60
A/dung tinh chat cua day ti so = nhau co:
\(\dfrac{x}{17}=\dfrac{y}{3}=\dfrac{x+y}{17+3}=-\dfrac{60}{20}=-3\)
=> \(\left\{{}\begin{matrix}x=-3\cdot17=-51\\y=-3\cdot3=-9\end{matrix}\right.\)
Cách 2: đặt: \(\dfrac{x}{17}=\dfrac{y}{3}=k\Rightarrow x=17k;y=3k\)
=> x + y = 17k + 3k = 20k = -60
=> k = -3
=> x = -3 . 17 = -51; y = -3 . 3 = 9
vậy.......
b/ c1: \(\dfrac{x}{19}=\dfrac{y}{21}\Rightarrow\dfrac{2x}{38}=\dfrac{y}{21}\) và 2x - y = 34
A/dụng t/c của dãy tỉ số = nhau có:
\(\dfrac{2x}{38}=\dfrac{y}{21}=\dfrac{2x-y}{38-21}=\dfrac{34}{17}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=38\\y=42\end{matrix}\right.\)
c2: đặt \(\dfrac{x}{19}=\dfrac{y}{21}=k\Rightarrow x=19k;y=21k\)
=> 2x -y = 2 . 19k - 21k = 38k - 21k = 17k = 34
=> k = 2
=> x = 2 . 19 = 38; y = 2 . 21 = 42
Vậy.........
c/ Cách 1: a/dụng t/c của dãy tỉ số = nhau:
\(\dfrac{X^2}{9}=\dfrac{y^2}{16}=\dfrac{x^2+y^2}{9+16}=\dfrac{100}{25}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=4\cdot9=36\\y^2=4\cdot16=64\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\\\left[{}\begin{matrix}y=8\\y=-8\end{matrix}\right.\end{matrix}\right.\)
vậy .....
c2: đặt: \(\dfrac{x^2}{9}=\dfrac{y^2}{16}=k\Rightarrow x^2=9k;y^2=16k\)
=> x2 + y2 = 9k + 16k = 25k = 100
=> k = 4
=> x2 = 36 ; y2 = 64
=> \(\left\{{}\begin{matrix}\left[{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\\\left[{}\begin{matrix}y=8\\y=-8\end{matrix}\right.\end{matrix}\right.\)
vậy.......
