SOLUTION: Given that x and y are integers and {{{sqrt(8sqrt(11)+27) = y-sqrt(x-2y)}}}, find {{{-y^x}}}

Question 1199848: Given that x and y are integers and , find
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

where a,b,c are integers and

Equate corresponding terms to form this system of equations

Use c = 11 and we get this slightly reduced system

which turns into

Through a bit of trial and error, or the substitution method, you should find these solutions
a = 4
b = 1

So,

... can be verified using WolframAlpha

and

At first things seem fine.
The 4 and y match up to show y = 4
But the square root terms do not match up fully.
The left hand side (LHS) has a positive square root, while the right hand side (RHS) has the square root as negative.
This is a contradiction that you'll need to ask your teacher about for further clarification.

If we ignored the positive and negative discrepancy, then we can equate radicands, plug in y = 4 and solve for x.
11 = x-2y
11 = x-2*4
11 = x-8
x = 11-8
x = 19

But as mentioned before, we run into a contradiction

It's possible your teacher made a typo somewhere.
I would ask them for clarification.

The tutor Edwin McCravy reached a similar conclusion in the link below.
https://www.algebra.com/algebra/homework/Radicals/Radicals.faq.question.1151181.html

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