if `loga/(b-c)=logb/(c-a)=logc/(a-b)` then find the value of `a^ab^bc^c`

If (loga)/(b-c) = (logb)/(c-a) = (logc)/(a-b) , then prove that a^(a)b^(b)c^(c)=1 .

If a+b+c=1 , ab+bc+ca=-2 and abc=1 then find the value of a^4+b^4+c^4

If a^2+b^2+c^2 = 25 and a+b+c=7 , then find the value of ab+bc+ca .

If log_b a log_c a+log_a blog_c b+log_a clog_b c=3(where a,b,c are different positive real number !=1) then find the value of abc

If a + b + c = 6 and ab+bc+ca= 12. find the value of a^2+b^2+c^2

if [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=lambda a^2b^2c^2 then find the value of lambda

If a^(2)+ab+b^(2) = b^(2) +bc +c^(2) where a ne b ne c then find the value of a+b+c .

If a+b+c=9 and ab+bc+ca=26, find the value of a^(2)+b^(2)+c^(2).

If a^(2)+b^(2)+c^(2)=19 and ab+bc+ca=3 Find the value of a+b+c