This has been discussed before but it is important...
a+b+c=4
a2+b2+c2=6
a3+b3+c3=8
Find [a4+b4+c4] where [] denotes G.I.F?
P.s:I know a method but i'm not sure if it's the shortest one to do this problem....thus sharing this...
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4 Answers
1357Answer is 7?
I also don't have the shorter method
Searching for it.....
1057answer is 7...
the method i know of is:
(a2+b2+c2)2=a4+b4+c4+2(a2b+b2c2+a2c2)
To find a2b+b2c2+a2c2
(ab+bc+ca)2=a2b+b2c2+a2c2+2abc(a+b+c)
now we just need the value of abc which can be found out by the relation..
a3+b3+c3-3abc=(a+b+c)(a2+b2+c2-ab-bc-ca)
2305Form a cubic equation having roots - a,b and c.Then use Vieta's formula and Newton's sums (http://wiki.artofproblemsolving.com/index.php/Newton%27s_Sums) to solve.Maybe that will be slightly faster.
Swarna Kamal Dhyawala vieta formulaUpvote·0· Reply ·2013-02-20 07:11:22- Swarna Kamal Dhyawala ??????
- Shaswata Roy @Swarna Kamal Dhyawala: Sir had done that in class.(Info on vieta's formulas:http://wiki.artofproblemsolving.com/index.php/Vieta%27s_formulas)