`|( (a^2 + b^2)/c, c, c), (a, (b^2 +c^2)/a, a), (b, b, (c^2 + a^2)/2)|` = 4abc

Prove: |((a^2+b^2)/c,c,c),( a,(b^2+c^2)/a ,a),( b,b,(c^2+a^2)/b)|=4a b c

For a non-/cro real a,b and c |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(c^2+a^2)/b)|=alpha abc, then the value of alpha is -

|((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A) 4abc (B) a^2+b^2+c^2 (C) (a+b+c)^2 (D) None of These

(a^(2)+b^(2))/(c),c,ca,(b^(2)+c^(2))/(a),ab,b,(c^(2)+a^(2))/(2)]|=4abc

show that [[(a^(2)+b^(2))/(c),c,ca,(b^(2)+c^(2))/(a),ab,b,(a^(2)+b^(2))/(c)]]=4abc

(b + c) ^ (2), ab, caab, (a + c) ^ (2), bcac, bc, (a + b) ^ (2)] | = 2abc (a + b + c) ^ ( 3)

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

If a^2+b^2+c^2+ab+bc+ca<=0 AA a, b, c in R then find the value of the determinant |[(a+b+2)^2, a^2+b^2, 1] , [1, (b+c+2)^2, b^2+c^2] , [c^2+a^2, 1, (c+a+2)^2]| : (A) abc(a^2 + b^2 +c^2) (B) 0 (C) a^3+b^3+c^3 + 3abc (D) 65