(sqrt(2)+1)^(5)+(sqrt(2)-1)^(5)

Evaluate (sqrt2+1)^(5))-(sqrt2-1)^(5) using binomial theorem.

The eccentricity of the ellipse if the distance between the foci is equal to the length of the latus rectum is (sqrt(5)-1)/(2) b.(sqrt(5)+1)/(2) c.(sqrt(5)-1)/(4) d.none of these

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))

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))

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

Find ( sqrt(5) + 1 )/( sqrt(5 ) - 1) = ( A ) ( 3 + sqrt(5) )/2 ( A ) ( 3 - sqrt(5) )/2 ( A ) ( 3 + sqrt(5) )/4 ( A ) ( 3 - sqrt(5) )/4

Find the values of x and y that satisfy the system of equations |x^(2)-2x|+y=1x^(2)+|y|=1-(A)(1-sqrt(5))/(2),(1-sqrt(5))/(2)(B)(1+sqrt(5))/(2),(1+sqrt(5))/(2)(C)(1-sqrt(5))/(2),(1+sqrt(5))/(2) (D) (1+sqrt(5))/(2),(1-sqrt(5))/(2)

[ If N=(sqrt(sqrt(5)+2)+sqrt(sqrt(5)-2))/(sqrt(sqrt(5)+1))-sqrt(3-2sqrt(2)) then N equals [ (A) 1, (B) 2sqrt(2)-1 (C) (sqrt(5))/(2), (D) (2)/(sqrt(sqrt(5)+1))]]