Divide a Number Problems

$\{\begin{array}{l}a+b=10\\ a^2=4\cdot (a\cdot b)\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ a^2=(1+\frac{1}{2})\cdot (a\cdot b)\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ 10^2=16\cdot a^2\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ 10^2=(6+\frac{1}{4})\cdot a^2\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{b}{a}=4\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ a^2=9b\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ a\cdot b=21\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {(a-b)}^2\cdot (7+\frac{1}{9})={(a\cdot b)}^2\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ [(a\cdot b)+a^2]\cdot a={[a\cdot (\frac{1}{2}\cdot a)]}^2+36\end{array}$

no such category found: #divide 10 into two parts