Gọi ba phần đó là a,b,c
=> 5a = 2b = 4c và a3 + b3 + c3 = 9512
\(5a=2b=4c\Rightarrow\dfrac{a}{\dfrac{1}{5}}=\dfrac{b}{\dfrac{1}{2}}=\dfrac{c}{\dfrac{1}{4}}\Rightarrow\dfrac{a^3}{\dfrac{1}{125}}=\dfrac{b^3}{\dfrac{1}{8}}=\dfrac{c^3}{\dfrac{1}{64}}\)
Áp dụng t/c của dãy tỉ số bằng nhau, ta có:
\(\dfrac{a^3}{\dfrac{1}{125}}=\dfrac{b^3}{\dfrac{1}{8}}=\dfrac{c^3}{\dfrac{1}{64}}=\dfrac{a^3+b^3+c^3}{\dfrac{1}{125}+\dfrac{1}{8}+\dfrac{1}{64}}=\dfrac{9512}{\dfrac{1189}{8000}}=64000\)
\(\Rightarrow\left\{{}\begin{matrix}a^3=\dfrac{64000}{125}=512\\b^3=\dfrac{64000}{8}=8000\\c^3=\dfrac{64000}{64}=1000\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=8\\b=20\\c=10\end{matrix}\right.\)
=> A = 8 + 20 + 10 = 38
