Menu Close

Question-101514




Question Number 101514 by bemath last updated on 03/Jul/20
Commented by Dwaipayan Shikari last updated on 03/Jul/20
(a+b+c)^2 =9  a^2 +b^2 +c^2 +2ab+2bc+2ac=9  a^2 +b^2 +c^2 −ab−bc−ca=3  (a+b+c)(a^2 +b^2 +c^2 −ab−bc−ca)=3.3=9  a^3 +b^3 +c^3 −3abc=9
(a+b+c)2=9a2+b2+c2+2ab+2bc+2ac=9a2+b2+c2abbcca=3(a+b+c)(a2+b2+c2abbcca)=3.3=9a3+b3+c33abc=9
Commented by Rasheed.Sindhi last updated on 03/Jul/20
(a+b+c)^2 =9  a^2 +b^2 +c^2 +2ab+2bc+2ac=9...(I)  a^2 +b^2 +c^2 −ab−bc−ca=3......(II)  (a+b+c)(a^2 +b^2 +c^2 −ab−bc−ca)=3.3=9  a^3 +b^3 +c^3 −3abc=9  Pl insert some steps between (I)  & (II).
(a+b+c)2=9a2+b2+c2+2ab+2bc+2ac=9(I)a2+b2+c2abbcca=3(II)(a+b+c)(a2+b2+c2abbcca)=3.3=9a3+b3+c33abc=9Plinsertsomestepsbetween(I)&(II).
Commented by mr W last updated on 03/Jul/20
a^2 +b^2 +c^2 +2ab+2bc+2ac=9...(I)  a^2 +b^2 +c^2 +2ab+2bc+2ac−6=9−6  a^2 +b^2 +c^2 +2ab+2bc+2ac−3(ab+bc+ca)=9−6  a^2 +b^2 +c^2 −ab−bc−ca=3......(II)
a2+b2+c2+2ab+2bc+2ac=9(I)a2+b2+c2+2ab+2bc+2ac6=96a2+b2+c2+2ab+2bc+2ac3(ab+bc+ca)=96a2+b2+c2abbcca=3(II)
Commented by Rasheed.Sindhi last updated on 03/Jul/20
Thamks sir mr W!
ThamkssirmrW!
Answered by Rasheed.Sindhi last updated on 03/Jul/20
a+b+c=3,ab+bc+ca=2  a^3 +b^3 +c^3 −3abc=?  In order to determine above we  need a^2 +b^2 +c^2   (a+b+c)^2 =(3)^2   a^2 +b^2 +c^2 +2(ab+bc+ca)=9  a^2 +b^2 +c^2 +2(2)=9  a^2 +b^2 +c^2 =5  Now,   a^3 +b^3 +c^3 −3abc    =(a+b+c)(a^2 +b^2 +c^2 −(ab+bc+ca))   =(3)(5−2)=9 ■
a+b+c=3,ab+bc+ca=2a3+b3+c33abc=?Inordertodetermineaboveweneeda2+b2+c2(a+b+c)2=(3)2a2+b2+c2+2(ab+bc+ca)=9a2+b2+c2+2(2)=9a2+b2+c2=5Now,a3+b3+c33abc=(a+b+c)(a2+b2+c2(ab+bc+ca))=(3)(52)=9◼
Commented by bemath last updated on 03/Jul/20
great sir. thank you
greatsir.thankyou
Answered by 1549442205 last updated on 07/Jul/20
a^3 +b^3 +c^3 =(a+b)^3 −3ab(a+b)+c^3 −3abc  =[(3−c)^3 +c^3 ]−3ab(a+b+c)=  (3+c−c)[(3−c)^2 −(3−c)c+c^2 ]−9ab  =3(9−6c+c^2 −3c+c^2 +c^2 )−9ab  =3(9−9c+3c^2 )−9ab=9(c^2 −3c+3−ab)  =9[c(−a−b)+3−ab]=9[3−(ab+bc+ca)]  =9(−2+3)=9  other way:a^3 +b^3 +c^3 −3abc=(a+b+c)^3   −3(a+b)(a+c)(b+c)−3abc=  3^3 −3[(3−a)(3−b)(3−c)]−3abc=  27−3[27−9(a+b+c)+3(ab+bc+ca)−abc]−3abc  =27−3(27−9.3+3.2−abc)−3abc  =27−3(6−abc)−3abc=27−18=9
a3+b3+c3=(a+b)33ab(a+b)+c33abc=[(3c)3+c3]3ab(a+b+c)=(3+cc)[(3c)2(3c)c+c2]9ab=3(96c+c23c+c2+c2)9ab=3(99c+3c2)9ab=9(c23c+3ab)=9[c(ab)+3ab]=9[3(ab+bc+ca)]=9(2+3)=9otherway:a3+b3+c33abc=(a+b+c)33(a+b)(a+c)(b+c)3abc=333[(3a)(3b)(3c)]3abc=273[279(a+b+c)+3(ab+bc+ca)abc]3abc=273(279.3+3.2abc)3abc=273(6abc)3abc=2718=9
Commented by Rasheed.Sindhi last updated on 03/Jul/20
First line:  a^3 +b^3 +c^3 −3abc=(a+b)^3 −3ab(a+b)+c^3 −3abc
Firstline:a3+b3+c33abc=(a+b)33ab(a+b)+c33abc
Commented by 1549442205 last updated on 05/Jul/20
Thank you sir.Excuse me as missed ”−3abc”
Thankyousir.Excusemeasmissed3abc

Leave a Reply

Your email address will not be published. Required fields are marked *