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

given x=(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3)),y=(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3)) find the value of x^(4)+y^(4)+(x+y)^(4)

(sqrt(5)+sqrt(3))(sqrt(7)-sqrt(3))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

(2sqrt(7))/(sqrt(5)-sqrt(3))

(sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))/(sqrt(7)-2sqrt(5))

(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))+(sqrt(8)+sqrt(7))/(sqrt(8)-sqrt(7))-(sqrt(8)-sqrt(7))/(sqrt(8)+sqrt(7))=a+b sqrt(14) Find the value of (a-b) (a) 8, (b) 16 (c) 4, (d) 0

Show that (i)" "{((3+2i))/((2-3i))+((3-2i))/((2+3i))} is purely real, (ii)" "{((sqrt(7)+i sqrt(3)))/((sqrt(7)-i sqrt(3)))+((sqrt(7)- i sqrt(3)))/((sqrt(7) + i sqrt(3)))} is purely real.

(sqrt(7)-sqrt(5))^3 - (sqrt(7)+sqrt(5))^3