OG详解-OG4 数学1 Q19

Choice C is correct. Dividing each side of the given equation by 2 yields 14x14y​=2√w+192​​, or xy​=√w+19​. Because it’s given that each of the variables is positive, squaring each side of this equation yields the equivalent equation(xy​)2​= w +19. Subtracting 19 from each side of this equation yields (xy​)2 - 19 = w, or w=(xy​)2​ -19. 
Choice A is incorrect. This equation isn’t equivalent to the given equation.
Choice B is incorrect. This equation isn’t equivalent to the given equation.
Choice D is incorrect. This equation isn’t equivalent to the given equation.