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.

Guest May 28, 2020

#1**0 **

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 = (x^{2} + 9) / x

The function: f(x) = (x^{2} + 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]

geno3141 May 28, 2020