`3/(sqrt(3)+1)+5/(sqrt(3)-1)`

Find the direction cosines of the line which is perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 . a) (1)/(sqrt(3)),(1)/(5sqrt(3)),(-7)/(5sqrt(3)) b) (5)/(sqrt(3)),(1)/(sqrt(3)),(7)/(5) c) (2)/(sqrt(3)),(5)/(2sqrt(3)),(1)/(7sqrt(3)) d) (1)/(sqrt(3)),(2)/(sqrt(3)),(-1)/(sqrt(3))

(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

Evalute: (sqrt(3)+1)^(5) -(sqrt(3)-1)^(5)

Simplify : (sqrt(3)+1)^(5)-(sqrt(3)-1)^(5)

Evaluate the following: (sqrt(3)+1)^(5)-(sqrt(3)-1)^(5)

Evaluate the following: \ (sqrt(3)+1)^5-(sqrt(3)-1)^5

Simplify the following (sqrt(3)+1)^(5) -(sqrt(3) -1)^(5)

If sqrt(2) = 1.414, sqrt(3) = 1.732, sqrt(5) = 2.236 and sqrt(6) = 2.449 , find the value of (2+sqrt(3))/(2-sqrt(3)) +(2-sqrt(3))/(2+sqrt(3)) +(sqrt(3) -1)/(sqrt(3) +1)