If `a_(1),a_(2),a_(3)` are the roots of the equation `8x^(3)+1001x+2008=0` then `(a_(1)+a_(2))^(3)+(a_(2)+a_(3))^(3)+(a_(3)+a_(1))^(3)` is equal to

If a_(1),a_(2),a_(3),a_(4) are are the roots of the equation 3x^(4)-(1+m)x^(3)+2x+5l=0 and Sigma a_(1)=3,a_(1),a_(2),a_(3),a_(4),=10 then (1,m)=

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) +a_(2))^(2) = (a_(1)-a_(4))^(2)

If a_(1),a_(2)...a_(n) are the first n terms of an Ap with a_(1)=0 and d!=0 then (a_(3)-a_(2))/(a_(2))+(a_(4)-a_(2))/(a_(3))+(a_(5)-a_(2))/(a_(4))...+(a_(n)-a_(2))/(a_(n-1)) is

If log (1-x+x^(2))=a_(1)x+a_(2)x^(2)+a_(3)x^(3)+… then a_(3)+a_(6)+a_(9)+.. is equal to

If z_(1),z_(2),z_(3),z_(4) are roots of the equation a_(0)z^(4)+a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=0, where a_(0),a_(1),a_(2),a_(3) and a_(4) are real,then

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(1),a_(2)...a_(n) are nth roots of unity then (1)/(1-a_(1))+(1)/(1-a_(2))+(1)/(1-a_(3))..+(1)/(1-a_(n)) is equal to

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to