given `x=(sqrt7+sqrt3)/(sqrt7-sqrt3) , y=(sqrt7-sqrt3)/(sqrt7+sqrt3) ` find the value of `x^4+y^4+(x+y)^4`

sqrt(7+4sqrt3) - sqrt(7-4sqrt3) =

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(2)

If x= (sqrt3+sqrt2)/(sqrt3-sqrt2) and y=(sqrt3-sqrt2)/(sqrt3+sqrt2) , then find the value of x^2+y^2

If (sqrt7-sqrt3)=1/sqrt5(sqrt(35)+x) , the value of x is:

(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3))-(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3))

Prove that [(sqrt7+i sqrt3)/(sqrt7-i sqrt3)+(sqrt7-i sqrt3)/ (sqrt7+i sqrt3)] is real.

Find: (sqrt7 +sqrt3)(3-sqrt3)

If x=(sqrt7+sqrt3)/(sqrt7-sqrt3) and xy=1 find the value of (x^2+y^2+5xy)/(x^2+y^2-5xy)

If sqrt (7 sqrt (7 sqrt7 sqrt7 sqrt7)) = 7 ^(x) then find the value of x