Answer:
[tex]\large \boxed{\sf \ \ \ x-y=-2\sqrt{7} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
it took me some time to understand the correct equations, I believe that you mean
[tex]x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176\sqrt{7}[/tex]
So let's play with these equations
[tex]x^4=y^4-176\sqrt{7}\\\\<=>y^4-x^4=176\sqrt{7}\\\\<=>y^4-x^4=(y^2)^2-(x^2)^2=(y^2-x^2)(y^2+x^2)=(y-x)(y+x)(x^2+y^2)\\\\=176\sqrt{7}[/tex]
So
[tex]x-y=-\dfrac{176\sqrt{7}}{(x+y)(x^2+y^2)}=-\dfrac{176\sqrt{7}}{4*22}=-2\sqrt{7}=-5.291503...[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
