Divide a Number Problems

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}$

no such category found: #divide 10 into two parts

$\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}$

no such category found: #divide 10 into two parts