Ta có : \(\frac{a}{2}=\frac{b}{3}-->\frac{a}{8}=\frac{b}{12}-->\frac{a^3}{512}=\frac{b^3}{1728}\)
\(\frac{b}{4}=\frac{c}{9}-->\frac{b}{12}=\frac{c}{27}-->\frac{b^3}{1728}=\frac{c^3}{19683}\)\(\left\{\frac{a^3}{512}=\frac{b^3}{1728}=\frac{c^3}{19683}}\)
ta có:
\(\frac{a}{2}=\frac{b}{3}\Rightarrow\frac{a}{2}:4=\frac{b}{3}:4\) hay \(\frac{a}{8}=\frac{b}{12}\left(1\right)\)
\(\frac{b}{4}=\frac{c}{9}\Rightarrow\frac{b}{4}:3=\frac{c}{9}:3\) hay \(\frac{b}{12}=\frac{c}{27}\left(2\right)\)
từ (1) và (2) \(\Rightarrow\frac{a}{8}=\frac{b}{12}=\frac{c}{27}\)
\(\frac{a}{8}=\frac{b}{12}=\frac{c}{27}=\frac{a^3+b^3+c^3}{8^3+12^3+27^3}=\frac{-1009}{21923}\)
\(\frac{a}{8}=\frac{-1009}{21923}\Rightarrow a=\frac{-8072}{21923}\) hay \(-0,368197783\)
\(\frac{b}{12}=\frac{-1009}{21923}\Rightarrow b=-0,552296674\)
\(\frac{c}{27}=\frac{-1009}{21923}\Rightarrow c=-1,242667518\)
vì \(a,b,c\notin Z\) nên \(\Rightarrow\) không thỏa mãn yêu cầu đề bài
bạn xem lại đề bài
