One has to throw a particle from one side of a fixed sphere, in a diameterical plane to another side such that it just grazes the sphere. Minimum possible speed for this is `sqrt(2gR(sqrt(alpha)+sqrt(beta)))`. Find `alpha+beta`

Evaluate the following intergrals : int sqrt((x-alpha)(beta-x))dx(alpha lt x lt beta)

If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta such that alpha , beta in N and (lambda)/(5) cancel in Z and lambda assumes minimum possible value then (sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|) is equal to

If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta such that alpha , beta in N and (lambda)/(5) cancel in Z and lambda assumes minimum possible value then (sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|) is equal to

If y=sqrt((t-alpha)/(beta-t)) and x=sqrt((t-alpha)(beta-t)) then find (dy)/(dx)

"If "int (1)/(sqrt(4x^(2)-5))dx=alpha log|x+sqrt(x^(2)-beta)|,"then "alpha+2beta is

The ratios of the length of the sides BC and AC of Delta ABC to the radius of circumscribea cirere are equal to 2 and respectively.If the ratio of the lengths of the bisectors of the interior angles B and C is (alpha(sqrt(alpha)-1))/(beta sqrt(gamma)) where alpha,beta,gamma in N, then find the value of (alpha+beta+gamma).

Find the quadratic polynomial for the zeroes, alpha , beta are, sqrt5,sqrt7 .

If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta such that alpha , beta in N and (lambda)/(5) cancel in Z and lambda assumes minimum possible value then (sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|) is equal to (a) (3)/(8) (b) (3)/(16) (c) (sqrt(111))/(34) (d) (sqrt(111))/(17)

If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta such that alpha , beta in N and (lambda)/(5) cancel in Z and lambda assumes minimum possible value then (sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|) is equal to (a) (3)/(8) (b) (3)/(16) (c) (sqrt(111))/(34) (d) (sqrt(111))/(17)