सरल कीजिए :
`(a+b+c)^(2) +(a-b+c)^(2) +(a+b-c)^(2)`

Prove that |{:((b+c)^(2), a^(2), bc),((c+a)^(2), b^(2), ca),((a+b)^(2), c^(2), ab):}|= (a-b) (b-c)(c-a)(a + b+c) (a^(2) + b^(2) + c^(2)) .

Given, a^(2) =b+c, b^(2)=c + a " & " c^(2) = a + b or (a^(2))/(b+c) = (b^(2))/(c+a) = (c^(2))/(a+b)=1 find (a)/(1+a) + (b)/(1+b) + (c )/(1+c) = ?

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

If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^2 then the value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)

If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c^2) then thhe value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)

If a^(2) +b^(2) +c^(2) = ab + bc + ca then ((a+b)/(c ) + (b+c)/(a) + (c+a)/(b)) ((c )/(a+b) + (b)/(a+c) + (c )/(a+b)) =?

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these