This is what I did
Can anyone tell me what's wrong me or the question?
Answer
You did the case y=4x, and got answers x=1 and x=−94. Neither is a solution of the original equation. It is easy to verify that when y=4x we have √xy−√yx=−32.
When you squared, you introduced extraneous roots. Only x=4y leads to a solution of the system.
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