Question

if a,b,c r such that a+b+c=2
a^2+b^2+c^2=6
a^3+b^3+c^3=8
then what is a^4+b^4+c^4 equal to?

Answer 1

Is it 9

Answer 2

no

Answer 3

OK D:

Answer 4

b =2 , c = 1, a = -1?

Answer 5

16 + 1 + 1 = 18

Answer 6

u r right @Ishaan94

Answer 7

Yay! but i would like to see algebraic solution.

Answer 8

so that was hit and trial?

Answer 9

Of course lol

Answer 10

You get the ab +ac+bc = 1 from an expansion of (a+b+c)^2

Answer 11

lolol i also solved it that way
i too m luking fr algebraic sol

Answer 12

@estudier , infact -1

Answer 13

The next expansion gives you zeros

Answer 14

@estudier just tell me how to use a^+b^2+c^2
the rest i can do myself

Answer 15

And I am too lazy to rearrange the expansion of ^4 into zeros, -1's and so:-)

Answer 16

i mean how to use the square terms to get a^4+b^4+c^4

Answer 17

Has anybody managed to find abc value? If yes, then the problem is solved algebraically

Answer 18

a*b*c = ?

Answer 19

-2

Answer 20

abc=-2

Answer 21

Ok. Then I am getting the answer algebraically. Typing below

Answer 22

@shivam_bhalla no need to type the whole sol.just tell how did u use a^+b^+c^ to get a^4+b^4+c^4

Answer 23

(a+b+c)^4 = (a^2 + b^2 + c^2 -2)(a^2 + b^2 + c^2 -2) = (a^2+b^2+c^2)^2 + 4 - 4(a^2+b^2+c^2)

= (a^4+b^4+c^4 + 2a^2b^2+ 2a^2c^2 + 2c^2b^2) + 4- 4*6

16 = a^4 + b^4 + c^4 + 2(a^2b^2+ a^2c^2 + c^2b^2) + 4 - 24

Answer 24

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab+2bc+2ca
(2)^2 = 6 + 2 (ab+bc+ca)
ab+bc+ca = -1

(a^2+b^2+c^2)^2 = a^4+b^4+c^4+2a^b^2+2b^2c^2+2c^2a^2
6^2 = a^4+b^4+c^4 + 2 ((ab+bc+ca)^2 - 2ab^2c-2abc^2-2a^2bc)
36 = a^4+b^4+c^4 + 2 ((-1)^2 - 2abc(b+c+a))
36 = a^4+b^4+c^4 + 2 (1 - 2(-2)(2))
a^4+b^4+c^4 = 18

Answer 25

What did FoolForMath mean by Newton's Identity?

Answer 26

idk

Answer 27

thanks a lot @shivam_bhalla

Answer 28

Welcome :D