If `a ,b , c` are nonzero real numbers such that `|b cc a a b c a a bb c a bb cc a|=0,t h e n` `1/a+1/(bomega)+1/(comega^2)=0` b. `1/a+1/(bomega^2)+1/(comega^)=0` c. `1/(aomega)+1/(bomega^2)+1/c=0` d. none of these

If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, a b,b c],[ a b,b c,c a]|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

If a ,\ b ,\ c are real numbers such that |b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0 , then show that either a+b+c=0 or, a=b=c .

(a+bomega+comega^(2))/(c+aomega+bomega^(2))

If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+b+c=2, then prove that a/(1-a)b/(1-b)c/(1-c)geq8

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

If omega ne 1 is a cube root of unity, then show that (a+bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+aomega+bomega^(2))=1

If a^3+b^3+6a b c=8c^3 & omega is a cube root of unity then: (a) a , b , c are in A.P. (b) a , b , c , are in H.P. (c) a+bomega-2comega^2=0 (d) a+bomega^2-2comega=0