I was simplifying the equation, $\sqrt{(x^2 + x)}xy = 5$, to, $\sqrt{(x^4 y^2 + x^3 y^2)} = 5$, using $\sqrt{(x)} x = \sqrt{(x^3)}$ but the graph appeared in all quadrants not just two and four. Can anyone explain why this happens and how to fix it?
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It is $$ab\sqrt{a^2+b^2}\ne \sqrt{a^2b^2(a^2+b^2)}$$ since we have $$\sqrt{x^2}=|x|$$
Dr. Sonnhard Graubner
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Then is there any way to simplify explain $\sqrt{x^2+x}xy$ down further – L. Kohler Apr 22 '19 at 20:10
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Only when you assume that $$xy\geq 0$$ then we get $$\sqrt{x^2+x}xy=\sqrt{x^2y^2(x^2+x)}$$ – Dr. Sonnhard Graubner Apr 22 '19 at 20:15
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@Dr. Sonnhard Graubner $xy$ is positif, otherwise LHS would not be equal to 5. – user376343 Apr 22 '19 at 21:12