Ta có :
\(\frac{a}{2}=\frac{b}{3};\frac{a}{4}=\frac{c}{9}\)
\(\Rightarrow\frac{a}{4}=\frac{b}{6}=\frac{c}{9}\)
\(\Rightarrow\frac{a^3}{64}=\frac{b^3}{216}=\frac{c^3}{729}\)
Áp dụng c/t tỉ lệ thức = nhau ta có :
\(\frac{a^3}{64}=\frac{b^3}{216}=\frac{c^3}{729}=\frac{a^3+b^3+c^3}{64+216+729}=\frac{-1009}{1009}=-1\)
\(\frac{a^3}{64}=-1\Rightarrow a^3=-64\Rightarrow a=-4\)\(\frac{b^3}{216}=-1\Rightarrow b^3=-216\Rightarrow a=-6\)\(\frac{c^3}{729}=-1\Rightarrow c^3=-729\Rightarrow a=-9\)Vậy a = -4 b = -6 c = -9