![i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc. i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc.](https://d10lpgp6xz60nq.cloudfront.net/question-thumbnail/en_32538276.png)
i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) If a^(2)+ b^(2)+c^(2)=250 " and" ab+bc+ca=3, " find" a+b+c. (iii) If a+b+c=11 and ab+ bc+ca=25, then find the value of a^(3)+b^(3)+c^(3)-3 abc.
![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)`( - YouTube 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)`( - YouTube](https://i.ytimg.com/vi/qZ4f3NzbS6Y/maxresdefault.jpg)
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)`( - YouTube
![radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange](https://i.stack.imgur.com/UVS3U.png)
radicals - Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$. - Mathematics Stack Exchange
How to prove [math]a^2+b^2+c^2-ab-bc-ca[/math] is non-negative for all values of [math] a, b,[/math] and [math]c - Quora
Using properties of determinants, prove that |(a,b,c)(a2,b2,c2)(bc,ca,ca)| = (a-b)(b-c)(c-a)(ab+bc+ca) - Sarthaks eConnect | Largest Online Education Community
How to prove [math]a^2+b^2+c^2-ab-bc-ca[/math] is non-negative for all values of [math] a, b,[/math] and [math]c - Quora
Prove the following identities –|(-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac)(a^2+ ab,b^2+ab,-ab)| = (ab + bc + ca)^3 - Sarthaks eConnect | Largest Online Education Community
![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) ( 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) (](https://d10lpgp6xz60nq.cloudfront.net/ss/web/129553.jpg)