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If AM of 2 numbersbe twice their GM then numbers are in the ratio

If AM of 2 numbersbe twice their GM then numbers are in the ratio

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
Let the numbers be a,b
AM=(a+b)/2
GM=\sqrt{ab}
Given AM=2GM
So (a+b)/2=2\sqrt{ab}
a+b-4\sqrt{ab}=0
Divide each term by b we get
(a/b)+1-4\sqrt{a/b}=0
(\sqrt{a/b})2-4(\sqrt{a/b})+1=0
on solving quadratic equation we get
\sqrt{a/b}=2\pm\sqrt{3}
So (a/b)=(2\pm \sqrt{3})2
(a/b)=7\pm 4\sqrt{3}

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