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

Interesting result!

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Guest Message by DevFuse

Started by BMAD, May 09 2013 09:13 PM

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

Interesting result!

Spoiler for Newton Raphson

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9 replies to this topic

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 10 May 2013 - 09:39 PM

Any Hint for me?

Posted 11 May 2013 - 12:45 AM

Spoiler for hint

Posted 11 May 2013 - 09:38 AM Best Answer

Interesting result!

Spoiler for Newton Raphson

*Vidi vici veni.*

Posted 11 May 2013 - 09:55 AM

Spoiler for hintSpoiler for

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 )

Posted 11 May 2013 - 06:33 PM

Spoiler for monic cubic equation approach

Posted 11 May 2013 - 06:38 PM

Spoiler for monic cubic equation approach

Spoiler for

Posted 11 May 2013 - 06:38 PM

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

http://m.youtube.com...feature=related

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.

http://m.youtube.com...feature=related

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

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

*Vidi vici veni.*

Posted 11 May 2013 - 06:38 PM

Spoiler for notice

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