(1)(5+sqrt(2i))/(1-sqrt(21))

Express the following in the form a+ib (i) (5+sqrt(2i))/(1-sqrt(2i)) (ii)

(5+sqrt(2)i)/(1-2sqrt(i))

A=(1,3,-2) is a vertex of triangle ABC whose centroid is G=(-1,4,2) then length of median through A is sqrt(21) 3sqrt(21) sqrt(21)/2 (3sqrt(21))/(2)

The true solution set of inequality (log)_((x+1))(x^2-4)>1 is equal to 2,oo) (b) (2,(1+sqrt(21))/2) ((1-sqrt(21))/2,(1+sqrt(21))/2) (d) ((1+sqrt(21))/2,oo)

Find the integral int(1)/(5-8x-x^(2))dx A. (1)/(2sqrt(21))log|(sqrt(21)+(x+4))/(sqrt(21)-(x+4))|+C .B. (1)/(2sqrt(21))log|(sqrt(21)-(x+4))/(sqrt(21)+(x+4))|+C C. (1)/(sqrt(21))log|((x+4)+sqrt(21))/((x+4)-sqrt(21))|+Cquad D. (1)/(sqrt(21))log|((x+4)-sqrt(21))/((x+4)+sqrt(21))|+C

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

The true solution set of inequality log_((x+1))(x^(2)-4)>1 is equal to 2,oo)(b)(2,(1+sqrt(21))/(2))((1-sqrt(21))/(2),(1+sqrt(21))/(2))(d)((1+sqrt(21))/(2),oo)

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))