`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

In Delta ABC with usual notation r_1/(bc)+r_2/(ca)+r_3/(ab) is

1/log_(ab)(abc)+1/log_(bc)(abc)+1/log_(ca)(abc) is equal to:

If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)

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

If a+b+c=1 , the greatest value of (ab)/(a+b)+(bc)/(b+c)+(ca)/(c+a) , is

Statement-1: If a, b, c are positive numbers in AP such that (1)/(ab)+(1)/(bc)+(1)/(ca)=1, then the least value of b is sqrt(3) . Statement-2: A.M.geG.M.

Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0