Statement-1: If `a,b,c in R` then `a^2b^2+b^2c^2+c^2a^2 >= abc(a+b+c)` Statement-2: Since `A.M. >= G.M => a^2b^2+b^2c^2 >= 2ab^2c.`

Statement-1: If a,b,c in R then a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)>=abc(a+b+c) Statement-2: since A.M.>=G*M rArr a^(2)b^(2)+b^(2)c^(2)>=2ab^(2)c

If ab+bc+ca=0 then prove that a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)=-2abc (a+b+c)

Resolve into factors a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) + 2abc

Statement-1: In a !ABC , (a+b+c)(tanA/2+tanB/2)=2c cotC/2 Statement-2: In a !ABC , a = b cos C + c cos B

Statement-1: In a !ABC , (a+b+c)(tanA/2+tanB/2)=2c cotC/2 Statement-2: In a !ABC , a = b cos C + c cos B

If a^2+b^2+c^2+ab+bc+ca<=0 AA a, b, c in R then find the value of the determinant |[(a+b+2)^2, a^2+b^2, 1] , [1, (b+c+2)^2, b^2+c^2] , [c^2+a^2, 1, (c+a+2)^2]| : (A) abc(a^2 + b^2 +c^2) (B) 0 (C) a^3+b^3+c^3 + 3abc (D) 65

Verify (a + b + c) (a ^(2) +b ^(2) + c ^(2) - ab - b c - ca) = a ^(3) + b ^(2) + c ^(2) - 3 abc

Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

Statement 1 If a,b,c are three positive numbers in GP, then ((a+b+c)/(3))((3abc)/(ab+bc+ca))=(abc)^((2)/(3)) . Statement 2 (AM)(HM)=(GM)^(2) is true for positive numbers.