Question

Tìm các số hữu tỉ a,b,c biết ab=2, bc=3, ac=54

Answer 1

\(\left\{{}\begin{matrix}ab=2\\bc=3\\ac=54\end{matrix}\right.\Rightarrow\left(abc\right)^2=2\cdot3\cdot54=324\)

\(\Rightarrow\left[{}\begin{matrix}abc=\sqrt{324}\\abc=-\sqrt{324}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}abc=18\\abc=-18\end{matrix}\right.\)

Nếu abc = 18

\(\Rightarrow\left\{{}\begin{matrix}c=\dfrac{18}{2}=9\\a=\dfrac{18}{3}=6\\b=\dfrac{18}{54}=\dfrac{1}{3}\end{matrix}\right.\)

Nếu abc = -18

\(\Rightarrow\left\{{}\begin{matrix}c=-\dfrac{18}{2}=-9\\a=-\dfrac{18}{3}=-6\\b=-\dfrac{18}{54}=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy \(\left(a,b,c\right)=\left(-6;-\dfrac{1}{3};-9\right);\left(6;\dfrac{1}{3};9\right)\)

Answer 2