Prove the following identities – |(b^2+c^2,ab,ac)(ba,c^2+a^2,bc)(ca,cb,a^2+b ^2)| = 4a^2b^2c^2 - Sarthaks eConnect | Largest Online Education Community
Prove the following identities – |(b^2+c^2,ab,ac)(ba,c^2+a^2,bc)(ca,cb,a^2+b ^2)| = 4a^2b^2c^2 - Sarthaks eConnect | Largest Online Education Community
![Factorise (i) a^2+b^2-2(ab-ac+bc) (ii) 4a^2-9b^2-(2a-3b) (iii) a-b-a2+b2 (iv) 108a^2-3(b-c)^2 - YouTube Factorise (i) a^2+b^2-2(ab-ac+bc) (ii) 4a^2-9b^2-(2a-3b) (iii) a-b-a2+b2 (iv) 108a^2-3(b-c)^2 - YouTube](https://i.ytimg.com/vi/n4O1UVLjfAU/maxresdefault.jpg)
Factorise (i) a^2+b^2-2(ab-ac+bc) (ii) 4a^2-9b^2-(2a-3b) (iii) a-b-a2+b2 (iv) 108a^2-3(b-c)^2 - YouTube
![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.
![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)
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, b, c are real, then f(x) = |((x + a^2), ab, ac), (ab, x + b^2, bc), ( ac, bc, x + c^2)| is decreasing in - Sarthaks eConnect | Largest Online Education Community
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
![prove that a^2 + b^2 + c^2 -ab -bc - ca is always non negative for all values of a, - Maths - Polynomials - 1213071 | Meritnation.com prove that a^2 + b^2 + c^2 -ab -bc - ca is always non negative for all values of a, - Maths - Polynomials - 1213071 | Meritnation.com](https://s3mn.mnimgs.com/img/shared/userimages/mn_images/image/a1(1523).png)