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        riddles >> medium >> Solvng in Radicals
        
(Message started by: Barukh on Nov 19th, 2007, 10:04am)
Title: Solvng in Radicals
Post by Barukh on Nov 19th, 2007, 10:04am
Solve in radicals:

http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(5-x) = x2 - 5.

Edited (fixed a typo).
Title: Re: Solvng in Radicals
Post by Joe Fendel on Nov 19th, 2007, 11:46am
Okay, I'll try this one:

[hideb]Square both sides to get
5 - x = x4 - 10x2 + 25

so we're solving for x4 - 10x2 + x + 20 = 0.  This factors into
(x2 - x - 4)(x2 + x - 5) = 0

Therefore the solutions can be obtained by the quadratic formula:

x = one of the following:
a) (1 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif17)/2
b) (1 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif17)/2
c) (-1 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif21)/2
d) (-1 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif21)/2
[/hideb]


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