Question

Answer 1

Gọi 3 số là a,b,c

Ta có \(\dfrac{a}{0,5}=\dfrac{b}{1\dfrac{2}{3}}=\dfrac{c}{2\dfrac{1}{4}}\Rightarrow\dfrac{a}{\dfrac{1}{2}}=\dfrac{b}{\dfrac{5}{3}}=\dfrac{c}{\dfrac{9}{4}}\)

Đặt \(\dfrac{a}{\dfrac{1}{2}}=\dfrac{b}{\dfrac{5}{3}}=\dfrac{c}{\dfrac{9}{4}}=k\Rightarrow a=\dfrac{1}{2}k;b=\dfrac{5}{3}k;c=\dfrac{9}{4}k\)

\(a^2+b^2+c^2=4660\\ \Rightarrow\dfrac{1}{4}k^2+\dfrac{25}{9}k^2+\dfrac{81}{16}k^2=4660\\ \Rightarrow\dfrac{1165}{144}k^2=4660\\ \Rightarrow k^2=576\\ \Rightarrow\left[{}\begin{matrix}k=24\\k=-24\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}a=12;b=40;c=54\\a=-12;b=-40;c=-54\end{matrix}\right.\)