Prove that `b^(2)c^(2) + c^(2)a^(2) + a^(2) b^(2) gt` abc (a+b+c)

If a,b, and c are non - zero real numbers, then Delta=|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)b^(2),ab,a+b)| is equal to a) abc b) a^(2)b^(2)c^(2) c)bc+ca+ab d)None of these

Prove that |(1+a^(2)+a^(4),1+ab+a^(2)b^(2),1+ac+a^(2)c^(2)),(1+ab+a^(2)b^(2),1+b^(2)+b^(4),1+bc+b^(2)c^(2)),(1+ac+a^(2)c^(2),1+bc+b^(2)c^(2),1+c^(2)+c^(4))|=(a-b)^(2)(b-c)^(2)(c-a)^(2)

The equation a cos theta + b sin theta = c has a solution when a,b and c are real numbers such that : a) a lt b lt c b) a = b=c c) c ^(2) lea ^(2) + b ^(2) d) c ^(2) le a ^(2) -b ^(2)

The value of the determinant |(bc,ac,ab),(a,b,c),(a^(3),b^(3),c^(3))| is a)(a + b + c) b)a + b + c -ab c) (a^(2) - b^(2))(b^(2) - c^(2)) (c^(2) - a^(2)) d) a^2+b^2+c^2

Suppose a ,b ,c are in A.P and a^(2) , b^(2) , c^(2) are in G.P. If a lt b lt c and a+b+c = (3)/(2) then the value of a is

Prove that tan((A-B)/2)= (a-b)/(a+b)cot frac(c)(2)

If a, b and c are distinct reals and the determinant |{:(a ^(3) +1, a ^(2) , a ),( b ^(3) +1, b ^(2) , b ),( c ^(3) +1, c ^(2), c):}|= 0, then the product abc is

Prove that |(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=-(a+b+c)xx(a-b)(b-c)(c-a).