[" 56."₫[a=(sqrt(3))/(2)vec e},vec i]sqrt(1+a)+sqrt(1-a)(1)/((11-a))(1)/(417)(1)/(841)?],[[" (a) "sqrt(3)," (b) "(sqrt(3))/(2)," (c) "(2+sqrt(3))," (d) "]]

(i)1/sqrt(2)+sqrt(3)+1/sqrt(2)

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

On the ellipse 2x^(2)+3y^(2)=1 the points at which the tangent is parallel to 4x=3y+4 are ( i )((2)/(sqrt(11)),(1)/(sqrt(11))) or (-(2)/(sqrt(11)),-(1)/(sqrt(11))) (ii) (-(2)/(sqrt(11)),(1)/(sqrt(11))) or ((2)/(sqrt(11)),-(1)/(sqrt(11))) (iii) (-(2)/(5),-(1)/(5)) (iv) ((3)/(5),(2)/(5)) or (-(3)/(5),-(2)/(5))

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

int_(-1)^(1//2)(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to a) (sqrt(e))/(2)(sqrt(3)+1) b) (sqrt(3e))/(2) c) sqrt(3e) d) sqrt(e/3)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

int_(-1)^((1)/(2))(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to (sqrt(e))/(2)(sqrt(3)+1) (b) (sqrt(3e))/(2)sqrt(3e)(d)sqrt((e)/(3))

The value of ((1+sqrt(3i))/(1-sqrt(3i)))^(64)+((1-sqrt(3i))/(1+sqrt(3i)))^(64) is -