`((4 +sqrt5)/(4-sqrt5)) +((4-sqrt5)/(4+sqrt5))` =?

Simplify: (4+\ sqrt(5))/(4-sqrt(5))+(4-\ sqrt(5))/(4+\ sqrt(5))

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

Evalutate : (4-sqrt(5))/(4+sqrt(5))+ (4+sqrt(5))/(4-sqrt(5))

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

Solve : (4-sqrt(5))/(4+sqrt(5))+ (2)/(5+sqrt(3))+(4+sqrt(5))/(4-sqrt(5))

If tan\ theta/2=(cosec theta-sin theta), then tan^2\ theta/2 may be equal to (A) 2-sqrt(5) (B) (9-4sqrt(5))(2+sqrt(5)) (C) -2+sqrt(5) (D) (9-4sqrt(5))(2-sqrt(5))

The equaiton of the line which bisects the obtuse angle between the lines x-2y+4=0 and 4x-3y+2=0 (A) (4-sqrt(5))x-(3-2(sqrt(5)) y+ (2-4sqrt(5))=0 (B) (3-2sqrt(5)) x- (4-sqrt(5))y+ (2+4(sqrt(5))=0 (C) (4+sqrt(5)x-(3+2(sqrt(5))y+ (2+4(sqrt(5))=0 (D) none of these

(3+sqrt5)^2 xx (3-sqrt5)^2 = ?

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

a=9-4sqrt(5) , sqrt(a)-1/sqrt(a)=?