[" 215"[a:b=b:c" - "225],[" (a) "(abc(a+b+e)^(3))/((ab+bc+ca)^(3))=1]]

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

Suppose a, b, c are three vectors such that abs(a)=abs(b)=abs(c)=1" and "a+b+c=0," then "abs(a-b)^(2)+abs(b-c)^(2)+abs(c-a)^(2)= _______

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

If a, b, c are in geometric progression, then show that, (a^(2) + ab + b^(2))/(ab + bc + ca) = (a + b)/(b + c)

If a:b = 3:5 and b:c = 6:7, find a:b:c

|(b^(2)-ab,b-c,bc-ac),(ab-a^(2),a-b,b^(2)-ab),(bc-ac,c-a,ab-a^(2))|=

det[[a,a^(2),bcb,b^(2),cac,c^(2),ab]]=(a-b)(b-c)(c-a)(ab+bc+ca)