" 11."quad (i)sqrt((a^(2)-x^(2))/(a^(2)+x^(2)))

Given I=int_(0)^(2)(sqrt((x^(4))/(4)-2x^(3)+(11)/(2)x^(2)-6x+4))dx then the value of I lie in the interval

The number of irrational solutions of the equation sqrt(x^(2)+sqrt(x^(2)+11))+sqrt(x^(2)-sqrt(x^(2)+11))=4 , is

The number of irrational solutions of the equation sqrt(x^(2)+sqrt(x^(2)+11))+sqrt(x^(2)-sqrt(x^(2)+11))=4 , is

(i) int(dx)/(sqrt(11-4x^(2)))

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

The expression (sqrt(x^(3)-1)+x^(2))^(11)-(sqrt(x^(3)-1)-x^(2))^(11) is a polynomial of degree

Let f(x)sqrt((1-x^(2))(1+2x^(2))) defined on [-1,1] then -