The real numbers x and y are such that
\begin{align*}
x + y &= 4, \\
x^2 + y^2 &= 22, \\
x^4 &= y^4 - 176 \sqrt{7}.
\end{align*}
Compute x-y
USE VIETA FORMULA
(If that big-brain user could come again that would be great :) )
+36916 Not sure how to use Vieta for this one
x+ y = 4
y = 4-x
x^2 + (4-x)^2 = 22
2x^2 - 8x - 6 = 0 x + y = -8/2 = 4 and xy = -6/2 = -3 (vieta .. just a check for the next step check)
by Quadratic Formula x = 2+- sqrt 7 (x+ y = 4 check x y = -3 check)
Since x^4 = y^4 - 176 sqrt 7 this tells me that y is the larger root 2 + sqrt7 and x = 2- sqrt 7
so x - y = 2-sqrt7 - (2 + sqrt7) = - 2 sqrt 7
Not sure if that is what you needed ! 
