Question 1209897
.
Let x and y be real numbers satisfying
\frac{x^2y^2 - 1}{2y - 1} = 4x + y.
Find the largest possible value of x.
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Use free of charge plotting tool DESMOS at web-site www.desmos.com/calculator


Print your equation in the calculator window.


It will show the plot instantly.


On the plot, click on the curve where you see the maximum in x.


The coordinate of this point is about x = 4.45252.


It is an approximate answer to the problem's question.



See my plot at this link

https://www.desmos.com/calculator/lqcjy9a296



Solved.



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In his post,  @CPhill gives  " the final answer "    {{{(17+sqrt(273))/8}}}.


This answer is incorrect,  since its numerical value is  4.190339,
 while the correct answer is close to  4.45252.


So,  once again @CPhill is deceiving readers.