Question

exercițiul 5, vă rog mult.

Answer 1

[tex]( \sqrt{x^2+xy} +x - \sqrt{xy} )( \sqrt{xy + y^2} - \sqrt{xy}+y ) = \\ = ( \sqrt{x(x+y)} +x - \sqrt{xy} )( \sqrt{y(x+y)} - \sqrt{xy}+y ) \\ = \sqrt{xy(x+y)^2} - \sqrt{x^2y(x+y)} +y\sqrt{x(x+y)} +x \sqrt{y(x+y)} - \\ x\sqrt{xy}+xy - \sqrt{xy^2(x+y)} +xy - y\sqrt{xy} \\ = (x+y) \sqrt{xy} - x\sqrt{y(x+y)}+y\sqrt{x(x+y)} +x \sqrt{y(x+y)} - \\ x\sqrt{xy}+xy - y\sqrt{x(x+y)} +xy - y\sqrt{xy} \\ = (x+y-x-y)\sqrt{xy} + (-x+x)\sqrt{y(x+y)}+(y-y)\sqrt{x(x+y)} + 2xy \\ = 2xy[/tex]