Đặt \(\frac{x}{3}=\frac{y}{4}=k\)
\(\Rightarrow\)\(x=3k;\)\(y=4k\)
Ta có: \(x^2\times y^2=144\)
\(\Leftrightarrow\)\(\left(3k\right)^2\times\left(4k\right)^2=144\)
\(\Leftrightarrow\)\(9k^2\times16k^2=144\)
\(\Leftrightarrow\)\(144k^4=144\)
\(\Leftrightarrow\)\(k^4=1\)
\(\Leftrightarrow\)\(k=\pm1\)
Nếu \(k=1\)thì \(x=3;\)\(y=4\)
Nếu \(k=-1\)thì \(x=-3;\)\(y=-4\)
Đặt x/3=y/4=k, suy ra x=3k;y=4k
Suy ra : (3k)^2+(4k)^2=144
9.k^2+16.k^2=144
25.k^2=144
k^2=5,76
Suy ra k= căn của 5,76 = 2,4 hay -2,4
Nếu k=2,4 suy ra x=7,2;y=9,6
Nếu k=-2,4 suy ra x=-7,2;y=-9,6
Vậy.......
