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Question

If the arithmetic mean of a and b is double their geometric mean, with a>b>0, then a possible value for the ratio a/b, to the nearest integer, is:

Accepted Answer

a+b2=2ab ab +1=4ab setting x=ab we get a quadratic equation isx^2+1=4x with solutions x=4 16-42 x^2=ab=(4+3)+43=13.8=14. 14