Let two numbers have arithmetic mean 9 and geometric mean 4.

Question

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation:

Accepted Answer

Let two numbers be a and b then $${{a + b} \over 2} = 9$$

and $$\sqrt {ab}  = 4$$

$$\therefore$$ Equation with roots $a$ and $b$ is

$${x^2} - \left( {a + b} \right)x + ab = 0$$

$$ \Rightarrow {x^2} - 18x + 16 = 0$$

Solutions · 1