If `a:b=2:3` and` a:c=1:2` then` b:c=?`

(i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac . (ii) If a^(2)+b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c . (iii) If a+b+c=11 and ab+bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc.

If A:B = 1:3 and B: C = 2:5. find A:C.

If A:B = 2:7 and B:C = 9:13, find A:C.

If A:B=3:4 and B:C=2:3 , find A:B:C .

If a+b+c=p and ab+bc+ac=q, find a^(2)+b^(2)+c^(2) .

If a+b+c=2, ab+bc+ca=-1 and abc=-2 , find the value of a^(3)+b^(3)+c^(3) .

If a, b and c are in H.P., then the value of ((ac+ab-bc)(ab+bc-ac))/(abc)^2 is

If A:B = 3:5 and B: C = 8:11, find A.C.

if a,and c are all non zero and a+b+c=0 , then prove that (a^(2))/(bc)+(b^(2))/(ac)+(c^(2))/(ab)=3.