If `c< 0 and ax^2 + bx + c = 0` does not have any real roots, then

If |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b)| then k=

If alpha=|(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|,beta=|(a,b,c),(b,c,a),(c,a,b)| , then

If a+b+c=0 , then the value of ((a+b)/(c)+(b+c)/(a)+(c+a)/(b)) ((a)/(b+c)+(b)/(c+a)+(c)/(a+b)) is

If a+b+c= 0, then the value of ((a+b)/c + (b+c)/a + (c+a)/b) ((a)/(b+c) + b/(c+a) + c/(a+b)) is :

If a+b+c= 0 , then ((a+b)/(c ) + (b+c)/(a) + (c+ a)/(b)) ((c )/(a+b) + (b)/(a+c) + (a)/(b+c)) = ?

If for z as real or complex,(1+z^(2)+z^(4))^(8)=C_(0)+C1z2+C2z4++C_(16)z^(32)then(a)C_(0)-C_(1)+C_(2)-C_(3)+C_(16)=1(b)C_(0)+C_(3)+C_(6)+C_(9)+C_(12)+C_(15)=3^(7)(c)C_(2)+C_(5)+C_(6)+C_(11)+C_(14)=3^(6)(d)C_(1)+C_(4)+C_(7)+C_(10)+C_(13)+C_(16)=3^(7)

If for z as real or complex, (1+z^2+z^4)^8=C_0+C1z2+C2z4++C_(16)z^(32)t h e n (a) C_0-C_1+C_2-C_3++C_(16)=1 (b) C_0+C_3+C_6+C_9+C_(12)+C_(15)=3^7 (c) C_2+C_5+C_6+C_(11)+C_(14)=3^6 (d) C_1+C_4+C_7+C_(10)+C_(13)+C_(16)=3^7

If for z as real or complex, (1+z^2+z^4)^8=C_0+C1z2+C2z4++C_(16)z^(32)t h e n (a) C_0-C_1+C_2-C_3++C_(16)=1 (b) C_0+C_3+C_6+C_9+C_(12)+C_(15)=3^7 (c) C_2+C_5+C_6+C_(11)+C_(14)=3^6 (d) C_1+C_4+C_7+C_(10)+C_(13)+C_(16)=3^7

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