Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the…
Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
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$x^2+18 x+16=0$
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$x^2-18 x-16=0$
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$x^2+18 x-16=0$
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$x^2-18 x+16=0$
Solution
Let numbers be $a, b \Rightarrow a+b=18, \sqrt{a b}=4 \quad \Rightarrow a b=16, a$ and $b$ are roots of the equation
$\Rightarrow \quad x^2-18 x+16=0$
Asked in: JEE Main 2004
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