# If A+B+C=0 And A2+B2+C2=1 , Then The Value Ofa4+B4+C4 Is?

I tried to lớn solve this problem, & I get \$a^4+b^4+c^4 = 2(a^2b^2 + 1)\$ but I"m not sure if it"s correct

\$egingroup\$ it would be better if you can write how did you get that part, then some body can trace errors (if there are any)... \$endgroup\$
Given \$a+b+c = 0\$ & \$(a^2+b^2+c^2) = 1\$, Now \$(a^2+b^2+c^2)^2 = 1^2 = 1\$

\$(a^4+b^4+c^4)+2(a^2b^2+b^2c^2+c^2a^2) = 1.................(1)\$

and from \$(a+b+c)^2 = 0\$,

we get \$displaystyle 1+2(ab+bc+ca) = 0Rightarrow (ab+bc+ca) = -frac12\$

again squaring both side , we get \$displaystyle (ab+bc+ca)^2 = frac14\$

\$displaystyle (a^2b^2+b^2c^2+c^2a^2)+2abc(a+b+c) = frac14Rightarrow (a^2b^2+b^2c^2+c^2a^2) = frac14\$

So put in eqn.... \$(1)\$ , we get

\$displaystyle (a^4+b^4+c^4)+2cdot frac14 = 1Rightarrow (a^4+b^4+c^4) = frac12\$

nội dung
Cite
Follow
answered Oct 13, 2013 at 8:38

juantheronjuantheron
50.4k1313 gold badges8686 silver badges229229 bronze badges
\$endgroup\$
1
add a comment |
3
\$egingroup\$
\$\$a+b+c=0Rightarrow c=-(a+b)\$\$\$\$1=a^2+b^2+(a+b)^2=2a^2+2ab+2b^2=2(a^2+ab+b^2)Rightarrow a^2+ab+b^2=frac12\$\$\$\$eginalign*a^4+b^4+c^4 &= a^4+b^4+(a^4+4a^3b+6a^2b^2+4ab^3+b^4)\&= 2(a^4+2a^3b+3a^2b^2+2ab^3+b^4)\&= 2(a^2(a^2+ab+b^2)+b^2(a^2+ab+b^2)+ab(a^2+ab+b^2))\&= a^2+ab+b^2=frac12endalign*\$\$

share
Cite
Follow
answered Oct 13, 2013 at 8:43

Dennis GulkoDennis Gulko
15.3k11 gold badge3434 silver badges5757 bronze badges
\$endgroup\$
add a comment |
0
\$egingroup\$
Given a+b+c=0a+b+c=0 and (a2+b2+c2)=1(a2+b2+c2)=1, Now (a2+b2+c2)2=12=1(a2+b2+c2)2=12=1(a4+b4+c4)+2(a2b2+b2c2+c2a2)=1.................(1)(a4+b4+c4)+2(a2b2+b2c2+c2a2)=1.................(1)and from (a+b+c)2=0(a+b+c)2=0,

we get 1+2(ab+bc+ca)=0⇒(ab+bc+ca)=−121+2(ab+bc+ca)=0⇒(ab+bc+ca)=−12again squaring both side , we get (ab+bc+ca)2=14(ab+bc+ca)2=14(a2b2+b2c2+c2a2)+2abc(a+b+c)=14⇒(a2b2+b2c2+c2a2)=14(a2b2+b2c2+c2a2)+2abc(a+b+c)=14⇒(a2b2+b2c2+c2a2)=14So put in eqn.... (1)(1) , we get

(a4+b4+c4)+2⋅14=1⇒(a4+b4+c4)=12

giới thiệu
Cite
Follow
answered Apr 18, 2016 at 14:15

Aman sengarAman sengar
1
\$endgroup\$
1
add a comment |

## Your Answer

Thanks for contributing an answer to lớn noithatvinhxuan.vnematics Stack Exchange!

Please be sure to lớn answer the question. Provide details & share your research!

But avoid

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Bạn đang xem: If a+b+c=0 and a2+b2+c2=1 , then the value ofa4+b4+c4 is?

Use noithatvinhxuan.vnJax lớn format equations. noithatvinhxuan.vnJax reference.

Xem thêm: Phim Ngược Chiều Nước Mắt Tập 4: Ghét Cũng Là Một Cách Thể Hiện Tình Cảm

To learn more, see our tips on writing great answers.

Xem thêm: Giải Bài 12 Trang 76 Sgk Toán 9 Tập 1 2 Trang 76 Sgk Toán 9 Tập 1

Draft saved
Draft discarded

### Sign up or log in

Sign up using Google
Sign up using Facebook
Sign up using thư điện tử and Password
Submit

### Post as a guest

Name
thư điện tử Required, but never shown

### Post as a guest

Name
e-mail

Required, but never shown

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to lớn our terms of service, privacy policy & cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.
Featured on Meta
Linked
19
Finding the fraction \$fraca^5+b^5+c^5+d^5a^6+b^6+c^6+d^6\$ when knowing the sums \$a+b+c+d\$ lớn \$a^4+b^4+c^4+d^4\$
12
\$ a+b+c=0, a^2+b^2+c^2=1\$ implies \$ a^4+b^4+c^4=frac12\$
Related
2
Confusion: I can solve rate problem using "1 pool per \$a\$ hours", but not "\$a\$ hours per pool".
1
Method for solving the equation \$3 + 5x^1/2 = 2x\$?
0
Riddle to lớn solve. Grouping of integers.
0
What does it mean lớn be equal?
0
2 degree polynomial problem
2
What type of equation is this called?
1
If \$log_ax=3\$ & \$log_bx=4\$, then what is \$log_abx\$?
2
Solve this system of equations for real numbers
3
Find \$b_32\$ if \$prod_n=1^32(1-z^n)^b_nequiv 1-2z pmodz^33\$ & \$b_nin oithatvinhxuan.vnbbZ^+\$
Hot Network Questions more hot questions

Question feed
Subscribe to RSS
Question feed to subscribe khổng lồ this RSS feed, copy & paste this URL into your RSS reader.

noithatvinhxuan.vnematics
Company
Stack Exchange Network
Site design / biệu tượng công ty © 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Rev2022.12.2.43073

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device & disclose information in accordance with our Cookie Policy.