`(3+sqrt(5))^n-3[((3+sqrt(5))^n)/3]`

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

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

Find the value of a and b if (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) =a + bsqrt(5)

((sqrt(5)-3))/((sqrt(5)-3))times((sqrt(5)-3))/((sqrt(5)+3))

Show that the integral part in each of the following is even. n in N . (i) (3 sqrt(3)+5)^(2n+1) (ii) (5sqrt(5)+11)^(2n+1)

The value of (7+3 sqrt5)/(3+sqrt5)-(7-3 sqrt5)/(3-sqrt5) lies between: (7+3 sqrt5)/(3+sqrt5)-(7-3 sqrt5)/(3-sqrt5) का मान किसके बीच में होगा

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

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

The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) +… is:

If sum_(i=1)^n(x_i+1)^2=9n and sum_(i=1)^n(x_i-1)^2=5n , then standard deviation of these 'n' observations (x_1) is: (1) 2sqrt(3) (2) sqrt(3) (3) sqrt(5) (4) 3sqrt(2)