Check if the statement is true (algebraic)

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The discussion revolves around a potential error in a textbook problem involving the equation x + y + √(x - y) = 2 + √6. The user believes the textbook's solution of x = 2 and y = -2 is incorrect, as substituting these values does not satisfy the equation. Instead, they found alternative values using Wolfram Alpha, yielding x ≈ 2.09974 and y ≈ 1.84974. Additionally, they propose solving the system of equations x + y = 2 and x - y = 6, which leads to different values of x and y. The user plans to address this discrepancy with their lecturer.
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Homework Statement


I came across this problem in my textbook, i think the answer is wrong. I checked on wolfram alpha and got different results.



Homework Equations


x+y+√(x-y)=2+√6



The Attempt at a Solution


The solutions in the book are x=2 y=-2, however when I substituted it into the equation i get 2=2+√6
The answer i got on wolfram alpha is x=2.09974 and y=1.84974, can anyone help confirm that the solution is wrong?
 
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So you could solve it by writing two equations in x and y:

x + y = 2

And

x - y = 6

What do you get?
 
y=-2 and x=4, so the answer in the book is wrong. Thanks, ill have to sort this out with my lecturer.
 

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