Inequalities

Question

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495

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Let x and y be real numbers such that \(x - \sqrt{x + 6} = \sqrt{y + 6} - y\).

Let m be the minimum value of x+y, and M be the maximum value of x+y. Enter the ordered pair (m, M).

Thanks for any tips, hints, or answers you provide, anything is appreciated.

catmg · Answer 1 · 2021-06-07T06:05:14

I tried, but couldn't figure out the answer. :((

x - sqrt(x+6) = sqrt(y+6) - y

x + y = sqrt(y+6) + sqrt(x+6)

I'm not sure if this is true, but I feel like the maximum value of x+y would be when x = y.

So x = y = 3, making x + y = 6.

=^._.^=