`1/(bc)+1/(ca)+1/(ab)=`

If a,b,c are in A.P then a+1/(bc), b+1/(ca), c+1/(ab) are in

The vertices of a triangle are (ab,(1)/(ab)),(bc,(1)/(bc)),(ca,(1)/(ca)) where a,b,c are roots of the equation x^(3)-3x^(2)+6x+1=0 then centroid is

If a,b,c are in A.P then a+(1)/(bc),b+(1)/(ca),c+(1)/(ab) are in

If a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.

If a,b,c are in A.P. prove that: (i) (ab)^(-1),(ca)^(-1) and (bc)^(-1) are also in A.P. (ii) (ab+ac)/(bc),(bc+ca)/(ca),(ca+cb)/(ab) are also in A.P.

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0

The value of the determinant |((1)/(a),1,bc),((1)/(b),1,ca),((1)/(c),1,ab)| is -