Question

System of equations...
(Attempt shown)

Answer 1

\[\Large \begin{array}{l}x - y = 18\\\ \sqrt x + \sqrt y = 6\\ \\ \\ \\ \\x = 18 + y\\\\\sqrt {18 + y} + \sqrt y = 6\\\\18 + y + 2\sqrt {18y + {y^2}} + y = 36\\2y + 2\sqrt {18y + {y^2}} = 36 - 18\\2\left( {y + \sqrt {18y + {y^2}} } \right) = 18\\\left( {y + \sqrt {18y + {y^2}} } \right) = 9\\{y^2} + 2y\sqrt {18y + {y^2}} + \left( {18y + {y^2}} \right) = 81\\2{y^2} + 18y + 2y\sqrt {18y + {y^2}} = 81\\2\left( {{y^2} + 9y + y\sqrt {18y + {y^2}} } \right) = 81\\\left( {{y^2} + 9y + y\sqrt {18y + {y^2}} } \right) = \frac{{81}}{2}\end{array}\] and this seems endless...

I think I have the answer, but I need steps ... http://www.wolframalpha.com/input/?i=x-y%3D18+%2C+sqrt%28x%29%2Bsqrt%28y%29%3D6

Answer 2

I'm sure there's a simplier solution... Is just that I'm doing something wrong, I have a few ways I've tried in my notebook, but I just got expanding it... not simplifying :(

Answer 3

better to move \[\sqrt{x}\] to the right hand side