Solve `(a+b+c)^2=a^2+b^2+c^2+2(ab-bc-ca)`

Find the product of (a+b+2c)(a^2+b^2+4c^2 -ab-2bc-2ca) . (a+b+2c)(a^2+b^2+4c^2 -ab-2bc-2ca) का गुणनफल ज्ञात करें ।

Simplify: (a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)

(a+omega b+omega^(2)c)(a+omega^(2)b+omega c)=a^(2)+b^(2)+c^(2)-ab-bc-ca

If a!=b!=c then prove that (a^(2)+b^(2)+c^(2))/(ab+bc+ca)>1

Prove that a^(2)+b^(2)+c^(2)-ab-bc-ca is always non-negative for all values of a,b and c.

Prove that a^(2)+b^(2)+c^(2)-ab-bc-ca is always non-negative for all values of a,b and c

Show that |((b+c)^2,a^2,bc),((c+a)^2,b^2,ca),((a+b)^2,c^2,ab)|=(a^2+b^2+c^2)(a+b+c)(a-b)(b-c)(c-a).