If `4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)`, where a,b,c are non-zero real numbers, then a,b,c are in GP.
Statement 2 If `(a_(1)-a_(2))^(2)+(a_(2)-a_(3))^(2)+(a_(3)-a_(1))^(2)=0`, then `a_(1)=a_(2)=a_(3),AA a_(1),a_(2),a_(3) in R`.

If |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=

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)

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_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in

If (a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in

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

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is eqiual to

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in