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The sums of fourth power numbers
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?
Posted 11 May 2013 - 09:38 AM Best Answer
Vidi vici veni.
Posted 11 May 2013 - 11:30 AM
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 )
Posted 11 May 2013 - 06:38 PM
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.
Vidi vici veni.
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