" how that "(a)/(b+c)+(b)/(c+a)+(c)/(a+b)>(3)/(2)

Prove that ((a)/(b)-(b)/(c))^(3)+((b)/(c)-(c)/(a))^(3)+((c)/(a)-(a)/(b))^(3)=(3(ca-b^(2))(ab-c^(2))(bc-a^(2)))/(a^(2)b^(2)c^(2))

If sides of triangle ABC are a,b and c such that 2b=a+c then (b)/(c)>(2)/(3)( b) (b)/(c)>(1)/(3)(b)/(c)<2 (d) (b)/(c)<(3)/(2)

a+b+c=6and(1)/(a)+(1)/(b)+(1)/(c)=(3)/(2), then find (a)/(b)+(b)/(c)+(b)/(a)+(b)/(c)+(c)/(a)+(c)/(b)

The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a) (a-b)(b-c)(c-a) (b) 3(a-b)(b-c)(c-a) (c) -3\ (a-b)(b-c)(c-a) (d) (a+b+c)(a^2+b^2+c^2-a b-b c-c a)

The expression (a-b)^(3)+(b-c)^(3)+(c-a)^(3) can be factorized as (a)(a-b)(b-c)(c-a)(b)3(a-b)(b-c)(c-a)(c)-3(a-b)(b-c)(c-a)(d)(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)

Prove that |(a+b, b, c), (b+c, c, a), (c+a, a, b)| = 3abc - a^3-b^3-c^3.

(a-b)^3 + (b-c)^3 + (c-a)^3=? (a) (a+b+c)(a^2+b^2+c^2-ab-bc-ac) (b) 3(a-b)(b-c)(c-a) (c) (a-b)(b-c)(c-a) (d)none of these

The value of [{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}/{(a-b)^3+(b-c)^3+(c-a)^3}] = (1) 3(a+b)(b+c)(c+a) (2) 3(a-b)(b-c)(c-a) (3) (a+b)(b+c)(c+a) (4) 1

Prove that |b c-a^2c a-b^2a b-c^2-b c+c a+a bb c-c a+a bb c+c a-a b(a+b)(a+c)(b+c)(b+a)(c+a)(c+b)|=3.(b-c)(c-a)(a-b)(a+b+c)(a b+b c+c a)