The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3+2sqrt2):(3-2sqrt2).`

Explanation

Let the two numbers are `a` and `b`


Thus their `GM = sqrt(ab)`


According to the given condition , `a+b=6sqrt(ab)`...(1)


Adding (1) and (2), we obtain `b=6sqrt(ab)-(3+2sqrt2)sqrt(ab)`


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