383(a2+b2+c2)2=a4+b4+c4+2(a2b2+a2c2+b2c2)
If a+b+c=3
and
a(^2)+b(^2)+c(^2)=5
and
a(^3)+b(^3)+c(^3)=7
what is the value of [a(^4)+b(^4)+c(^4)] ??
And how is it done?
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4 Answers
21for only three no.s 0,1 and 2 the equality holds true.
Therefore, a4+b4+c4=04+14+24=17
There must be other ways to do it...but I do not know them...could anyone show me any other method please..?
- Anurag Choudhury Should a^3 + b^3 +c^3 be 7 or 9?
Upvote·0· Reply ·2012-09-15 09:51:11
- Anurag Choudhury sorry my mistake did not read the question properly... :{
21Also...
(a+b+c)2=a2+b2+c2 + 2(ab+bc+ca)
→9=(5+2x)
→2x=4
→x=2
→(ab+bc+ca)=2
Now,
a3+b3+c3-3abc=(a+b+c)(a2+b2+c2-ab-bc-ca)
→7-3abc=3(5-2)
→(-2)=3abc
→(-2/3)=abc
(a2+b2+c2)2=a4+b4+c4 +2abc(a+b+c)
→25=a4+b4+c4 +(-4/3)*3
→25=a4+b4+c4-4
→a4+b4+c4=29
- Anurag Choudhury Damn it...again made a mistake!
21(ab+bc+ca)2=4
→a2b2+b2c2+c2a2 + 2abc(a+b+c)=4
→a2b2+b2c2+c2a2 +(-4/3)(3)=4
→a2b2+b2c2+c2a2=8
Now you can do it...(a2+b2+c2)2=a4+b4+c4 +2(8)=25
→a4+b4+c4=9
- Anurag Choudhury Actually I did this sum at 11 in the night...brain was not functioning properly @ that time... :P :P
- Soumyabrata Mondal hmm... ;)
- Anurag Choudhury so..9 is the answer, right?
- Soumyabrata Mondal yap