Let a,b,c be positive integers, such that `|[b+c,c,b],[c,c+a,a],[b,a,a+b]|=8`, `a^(3)+b^(3)+c^(3)-3abc ` =

If a, b, c are distinct positive integers such that ab+bc+cage74 , then the minimum value of a^(3)+b^(3)+c^(3)-3abc, is

Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(3)

Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c

Prove that : |{:(a,b,c),(b,c,a),(c,a,b):}|=3 a b c-a^(3)-b^(3)-c^(3)

Let a,b ,c be positive integers such that b/a is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of (a^2+a-14)/(a+1) is

Let a,b ,c be positive integers such that b/a is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of (a^2+a-14)/(a+1) is

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3

Prove: \ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

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