1:
Để đây là 1 cấp số nhân thì
\(\left[{}\begin{matrix}\left(2a-1\right)^2=a\left(2a+1\right)\\a^2=\left(2a-1\right)\left(2a+1\right)\\\left(2a+1\right)^2=a\left(2a-1\right)\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}4a^2-4a+1-2a^2-a=0\\4a^2-1-a^2=0\\4a^2+4a+1-2a^2+a=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2a^2-5a+1=0\\3a^2-1=0\\2a^2+5a+1=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}a=\dfrac{5\pm\sqrt{17}}{4}\\a=\pm\dfrac{\sqrt{3}}{3}\\a=\dfrac{-5\pm\sqrt{17}}{4}\end{matrix}\right.\)
2:
Để đây là 1 cấp số nhân thì
\(\left[{}\begin{matrix}\left(2b+3\right)^2=7\cdot49\\7^2=49\left(2b+3\right)\\49^2=7\left(2b+3\right)\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\left(2b+3\right)^2=343\\2b+3=1\\2b+3=343\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}b=-1\\b=170\\2b+3=\pm7\sqrt{7}\end{matrix}\right.\)
=>\(b\in\left\{-1;170;\dfrac{7\sqrt{7}-3}{2};\dfrac{-7\sqrt{7}-3}{2}\right\}\)
