SOLUTION: prove that the sum of a positive real number and its reciprocal is at least two.

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Question 353502: prove that the sum of a positive real number and its reciprocal is at least two.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
n%2B1%2Fn=M
n%5E2%2B1=Mn
n%5E2-Mn%2B1=0
In order for the quadratic equation to have a real solution, the discriminant must be greater than or equal to 0.
b%5E2-4ac=M%5E2-4%281%29%281%29=M%5E2-4%3E=0
M%5E2%3E=4
highlight%28M%3E=2%29