Pyramid 821
Preview $$U_{821}(x, y) = \left(x \sqrt{4 y + 1} + 1\right)^{2}$$
Pyramid 822
Preview $$U_{822}(x, y) = x \left(y + 1\right) + \left(y + 1\right)^{4}$$
Pyramid 823
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Preview $$U_{823}(x, y) = \left(\frac{2 \sqrt{3} x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + 1\right)^{2}$$
Pyramid 824
Preview $$U_{824}(x, y) = \frac{- 4 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 3 y - \sqrt{- 24 \sqrt{3} x y^{\frac{3}{2}} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 9 y^{2}}}{8 x^{2} \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Pyramid 825
Preview $$U_{825}(x, y) = \frac{1}{\left(- \frac{2 \sqrt{3} x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + 1\right)^{2}}$$
Pyramid 826
Preview $$U_{826}(x, y) = \frac{1}{- x y + 1}$$
Pyramid 827
Preview $$U_{827}(x, y) = \frac{x y - 1}{x y + x - 1}$$
Pyramid 828
Preview $$U_{828}(x, y) = \frac{x y - \sqrt{x^{2} y^{2} - 2 x y - 4 x + 1} + 1}{2 x y + 2 x}$$
Pyramid 829
Preview $$U_{829}(x, y) = \frac{1 - \sqrt{- 4 x y^{5} - 20 x y^{4} - 40 x y^{3} - 40 x y^{2} - 20 x y - 4 x + 1}}{2 x y + 2 x}$$
Pyramid 830
Preview $$U_{830}(x, y) = \frac{1}{\left(1 - y\right)^{2} \left(- \frac{x}{1 - y} + 1\right)}$$
Pyramid 831
Preview $$U_{831}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{1 - y} + 1\right)}$$
Pyramid 832
Preview $$U_{832}(x, y) = \frac{- y^{2} + 2 y + \sqrt{- 4 x + y^{4} - 4 y^{3} + 6 y^{2} - 4 y + 1} - 1}{2 x y - 2 x}$$
Pyramid 833
Preview $$U_{833}(x, y) = \frac{x \left(1 - y\right)^{2} + 1}{\left(1 - y\right)^{3}}$$
Pyramid 834
Preview $$U_{834}(x, y) = \frac{1}{\left(1 - y\right)^{4} \left(- \frac{x}{1 - y} + 1\right)}$$
Pyramid 835
Preview $$U_{835}(x, y) = \frac{- y^{3} + 3 y^{2} - 3 y - \sqrt{- 4 x + y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} + y \left(4 x - 6\right) + 1} + 1}{2 x y^{2} - 4 x y + 2 x}$$
Pyramid 836
Preview $$U_{836}(x, y) = \frac{x \left(1 - y\right)^{3} + 1}{\left(1 - y\right)^{4}}$$
Pyramid 837
Preview $$U_{837}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{\left(1 - y\right)^{2}} + 1\right)}$$
Pyramid 838
Preview $$U_{838}(x, y) = \frac{y^{3} - 3 y^{2} + 3 y + \sqrt{- 4 x + y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} + y \left(4 x - 6\right) + 1} - 1}{2 x y - 2 x}$$
Pyramid 839
Preview $$U_{839}(x, y) = \frac{x y - x - 1}{y^{3} - 3 y^{2} + 3 y - 1}$$
Pyramid 840
Preview $$U_{840}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right) + 1}\right) \left(y + 1\right)}{2 x}$$
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