a,b,c là ba số hạng của cấp số nhân
=>\(b=ak;c=ak^2\)
\(\left\{{}\begin{matrix}a+b+c=14\\abc=64\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}a+ak+ak^2=14\\a\cdot ak\cdot ak^2=64\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a\left(k^2+k+1\right)=14\\a^3\cdot k^3=64\\\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}ak=4\\a=\dfrac{14}{k^2+k+1}\\\end{matrix}\right.\Leftrightarrow\dfrac{4}{k}=\dfrac{14}{k^2+k+1}\)
=>\(4k^2+4k+4-14k=0\)
=>\(4k^2-10k+4=0\)
=>\(2k^2-5k+2=0\)
=>(k-2)(2k-1)=0
=>\(\left[{}\begin{matrix}k=2\\k=\dfrac{1}{2}\end{matrix}\right.\)
TH1: k=2
\(a=\dfrac{4}{k}=\dfrac{4}{2}=2\)
\(b=2\cdot2=4;c=2\cdot2^2=8\)
TH2: k=1/2
\(a=4:k=4:\dfrac{1}{2}=8\)
\(b=8\cdot\dfrac{1}{2}=4;c=8\cdot\left(\dfrac{1}{2}\right)^2=2\)