`a=sqrt((3+sqrt5)/2), r=1/sqrt((1+sqrt5)/2)` and `S_(oo)=lambda/(sqrt5 -1)^3` then find the value of `lambda`

If a=(3+sqrt5)/2 then find the value of a^2+1/a^2

If x=(sqrt5+sqrt2)/(sqrt5-sqrt2) and y=(sqrt5-sqrt2)/(sqrt5+sqrt2) then find the value of (3x-2y)(x+2y)

If a = (sqrt5 +1)/(sqrt5-1) and b = (sqrt5-1)/(sqrt5+1) then find the value of (5a^(2) -3ab +5b^(2))

1/(sqrt5 +sqrt3 +2) + 1/(-sqrt5 +sqrt3 +2 ) =

If x = (sqrt5 -1)/(sqrt5 +1) and y (sqrt5 +1)/(sqrt5-1) then find the value of (x^(2)/y + y^(2)/x)

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

sqrt((3+sqrt(5))/(2)),sgn(x^(2)-3x+4) and 2{[(2)/(3+x^(2))]+sin((pi)/(10))},x in R are the first three consecutive terms of G.P.and sum of its infinite terms is (lambda)/((sqrt(5)-1)^(3)), then find the value of lambda