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

Question

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

Smart Achievers · Accepted Answer

(2)

$Given, arithmetic mean of x and y is 9 .$

$i.e., \frac{x + y}{2} = 9 \Rightarrow x + y = 18$

Geometric mean of $x$ and $y$ is 4, i.e., $\sqrt{x y} = 4 \Rightarrow x y = 16$

Now, sum of roots $(x + y) = 18$

Product of roots $(x y) = 16$

$∴$ Required quadratic equation is $x^{2} - 18 x + 16 = 0$

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