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yx+(2*√(xy)-x)y equation
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The solution
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/ _____ \ y*x + \2*\/ x*y - x/*y = 0
$$x y + y \left(- x + 2 \sqrt{x y}\right) = 0$$
Detail solution
Given the equation:
$$x y + y \left(- x + 2 \sqrt{x y}\right) = 0$$
transform:
Take common factor from the equation
$$2 y \sqrt{x y} = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$2 y = 0$$
$$x y = 0$$
solve the resulting equation:
1.
$$2 y = 0$$
Divide both parts of the equation by 2
We get the answer: y1 = 0
2.
$$x y = 0$$
Divide both parts of the equation by x
We get the answer: y2 = 0
The final answer:
$$y_{1} = 0$$
$$y_{2} = 0$$
$$x y + y \left(- x + 2 \sqrt{x y}\right) = 0$$
transform:
Take common factor from the equation
$$2 y \sqrt{x y} = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$2 y = 0$$
$$x y = 0$$
solve the resulting equation:
1.
$$2 y = 0$$
Divide both parts of the equation by 2
y = 0 / (2)
We get the answer: y1 = 0
2.
$$x y = 0$$
Divide both parts of the equation by x
y = 0 / (x)
We get the answer: y2 = 0
The final answer:
$$y_{1} = 0$$
$$y_{2} = 0$$
The graph