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Let x and y be real numbers such that xy=9. Find the set of all possible values of x+y. Enter your answer in interval notation.

 May 28, 2020
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Find the set of all possible values of  x + y  that fulfill  x·y  =  9.

 

When  x·y  =  9  . --->   y  =  9 / x      and     x + y  =  x + 9 / x   --->    x + y  =  (x2 + 9) / x

 

The function:  f(x)  =  (x2​ + 9) / x

--  has a minimum in the first quadrant at 6, so its positive values are in  [6, infinity)

--  has a maximum in the thrid quadrant at -6, so its negative values are in (- infinity, -6]

 May 28, 2020

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