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# The sums of fourth power numbers

Best Answer bonanova, 11 May 2013 - 09:38 AM

Interesting result!

Spoiler for Newton Raphson
Go to the full post

9 replies to this topic

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Posted 09 May 2013 - 09:13 PM

The sum of three numbers is 6, the sum of their squares is 8, and the sum of their cubes is 5. What is the sum of their fourth powers?

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### #2 dark_magician_92

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Posted 10 May 2013 - 09:39 PM

Any Hint for me?

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Posted 11 May 2013 - 12:45 AM

Spoiler for hint

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### #4 bonanova

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Posted 11 May 2013 - 09:38 AM   Best Answer

Interesting result!

Spoiler for Newton Raphson

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Vidi vici veni.

### #5 TimeSpaceLightForce

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Posted 11 May 2013 - 09:55 AM

Spoiler for hint
Spoiler for

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### #6 dark_magician_92

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Posted 11 May 2013 - 11:30 AM

Interesting result!

Spoiler for Newton Raphson

It appeared to me too that a,b,c all cant be real. If we could find the value of a*b*c, then the problem could be done. Can you please provide a link for newton raphson method (some easy explanation )

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Posted 11 May 2013 - 06:33 PM

Spoiler for monic cubic equation approach

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### #8 dark_magician_92

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Posted 11 May 2013 - 06:38 PM

Spoiler for monic cubic equation approach

Spoiler for

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### #9 bonanova

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Posted 11 May 2013 - 06:38 PM

dm92 asks for info on Newton method. Several links out there, this one is OK.

Successive approximations.

You solve f(x)=0. You give an initial guess x0. Then x1 = x0 - f(x0)/f'(x0). Repeat.

In several dimensions, like this problem with real numbers a x and y, the functions are
f1 = 6-sum abc
f2 = 8-sum2 abc
f3 = 5-sum3 abc

Calculate a 3x3 matrix M of partial derivatives of f123 wrt axy

Guess axy, and repeat axy = axy - M-1 x f123

You can use delta's to approximate the derivatives if f is messy.
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Vidi vici veni.

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Posted 11 May 2013 - 06:38 PM

Spoiler for notice

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