सिद्ध कीजिए:
`|{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c).`

Prove that : |{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c)

Prove that : |{:(x+a,b,c),(a,x+b,c),(a,b,x+c):}|=x^(2)(x+a+b+c)

|{:(x+a," "b," "c),(" "a,x+b," "c),(" "a," "b,x+c):}|=0

S.T abs[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=x^2(x+a+b+c)

Using the properties of determinants, prove that : |[[x+a,b,c],[a,x+b,c],[a,b,x+c]]| = x^2(x+a+b+c)

|{:(a-x," "b," "c),(" "b,c-x," "a),(" "c," "a,b-x):}|=0

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

If a ,\ b ,\ c are real numbers, then find the intervals in which f(x)=|(x+a^2,a b, a c),( a b, x+b^2,b c),( a c, b c, x+c^2)| is increasing or decreasing.

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these