Divide a Number Problems

Divide Ten into Two Parts

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

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

$\{\begin{array}{l}a+b=10\\ \frac{b}{a}=5\end{array}$

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

$\{\begin{array}{l}a+b=10\\ b^2-a^2=50\end{array}$

no such category found: #divide 10 into two parts

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

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {(a-b)}^2=20+\frac{1}{4}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {(b-a)}^2-a^2=32\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ 3a=b\cdot \sqrt{8}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {(a-b)}^2\cdot a=(20+\frac{1}{4})a\end{array}$

no such category found: #divide 10 into two parts

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

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

$\{\begin{array}{l}a+b=10\\ a+2\sqrt{a}=b-2\sqrt{b}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{array}$

no such category found: #divide 10 into two parts

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

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{40}{a}\cdot \frac{40}{b}=100\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ \frac{50}{a}\cdot \frac{40}{b}=125\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {\left(\frac{10}{a}\cdot \frac{10}{b}\right)}^2=20+\frac{1}{4}\end{array}$

no such category found: #divide 10 into two parts

$\{\begin{array}{l}a+b=10\\ {\left(\frac{40}{a}\right)}^2+{\left(\frac{40}{b}\right)}^2=625\end{array}$

no such category found: #divide 10 into two parts

Divide Ten into Three Parts

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

no such category found: #divide 10 into three parts