Have you tried Jensen's?
Algebra
Level
2
I have two numbers. The arithmetic mean and the geometric mean of these two numbers are equal. Which of the following is true?
They are not equal to each other
They are equal to each other
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Let these two numbers be x and you. Setting the two averages equal: (x+y)/2=sqrt (xy) Squaring both sides: (x^2+2xy+y^2)/4=xy Multiplying both sides by four and rearranging terms: x^2-2xy+y^2=0 Factoring and taking thr square root of both sides: x-y=0 This implies that: x=y