Question

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

• A. $x^2 - 18x - 16 = 0$
• B. $x^2 - 18x + 16 = 0$
• C. $x^2 + 18x - 16 = 0$
• D. $x^2 + 18x+ 16= 0$

Answer 1

Answer: (B)

$x^2 - 18x + 16 = 0$

Answer 2

We have,
$AM$ of $x, y=9$ and $GM$ of $x, y=4$
$\therefore \frac{x+y}{2}=9$ and $\sqrt{x y}=4$
$\Rightarrow x+y=18$ and $x y=16$
$\Rightarrow y=18-x$ and $x y=16$
$\therefore x(18-x)=16$
$\Rightarrow 18 x-x^{2}=16$
$\Rightarrow x^{2}-18 x+16=0$
$\therefore x$ and $y$ are the roots of the equation
$x^{2}-18 x+16=0$