Question

The real numbers x and y are such that x + y &= 4 x^2 + y^2 &= 22 x^4 = y^4 - 176 \sqrt{7}. Compute x - y.

PLEASE HELP ASAP

Answer 1

`\large \boxed{\sf \ \ \ x-y=-2√(7) \ \ \ }`

Explanation:

Hello,

it took me some time to understand the correct equations, I believe that you mean

`x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176√(7)`

So let's play with these equations

`x^4=y^4-176√(7)\\\\<=>y^4-x^4=176√(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√(7)`

So

`x-y=-(176√(7))/((x+y)(x^2+y^2))=-(176√(7))/(4*22)=-2√(7)=-5.291503...`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you