find two numbers whose arithmetic mean is 10 and geometric mean is 8​

Answer:4 and 16Step-by-step explanation:Let a and b be two unknown numbers.1. The arithmetic mean of these numbers is [tex]\dfrac{a+b}{2}=10[/tex]2. The geometric mean of these numbers is [tex]\sqrt{ab}=8[/tex]Solve the system of two equations:[tex]\left\{\begin{array}{l}\dfrac{a+b}{2}=10\\ \\\sqrt{ab}=8\end{array}\right.\Rightarrow \left\{\begin{array}{l}a+b=20\\ \\ab=64\end{array}\right.[/tex]From the first equation[tex]a=20-b[/tex]Substitute it into the second equation[tex](20-b)b=64\\ \\20b-b^2=64\\ \\-b^2+20b-64=0\\ \\b^2-20b+64=0\\ \\D=(-20)^2-4\cdot 64=400-256=144\\ \\b_{1,2}=\dfrac{-(-20)\pm \sqrt{144}}{2}=\dfrac{20\pm 12}{2}=16,\ 4[/tex]When [tex]b=16,\ a=20-b=20-16=4[/tex]When [tex]b=4,\ a=20-b=20-4=16[/tex]