If, a,b,c are positive and unequal,show that value of the determinant
`Delta ={:[( a,b,c),( b,c,a),( c,a,b)]:} ` is negative

|(a,b,c),(b,c,a),(c,a,b)| =

The value of the determinant {:abs((1,a,b+c),(1,b,c+a),(1 , c,a+b)):} is

The value of determine |{:(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c):}| is

The value of determinant |(a-b ,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is

If a, b, c are in G.P then the value of the determinant Delta= [[a, b, ax+by],[b ,c ,b x+c y],[a x+b y, b x+c y, 0]] is

If a , b , c are unequal , what is the condition that value of the following determinant is zero ? Delta=|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

Find the area of the triangle Delta ABC with A(a,b+c), B(b,c+a), and C(c, a+ b).

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2