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        riddles >> medium >> solve 2
        
(Message started by: tony123 on Jun 29^th, 2007, 6:46am)

Title: solve 2
Post by tony123 on Jun 29^th, 2007, 6:46am

sqrt(5 - x) +x^2 = 5

Title: Re: solve 2
Post by jollytall on Jun 29^th, 2007, 12:01pm

if you do:
sqrt(5-x) = 5-x²
then squere it (requires 5-x>0 and 5-x²>0, see backtesting later)
5-x=25-10x²+x⁴
then
x⁴-10x²+x+20=0
or
(x²+x-5)*(x²-x-4)=0
then from here you have four potential solutions.
All the four have 5-x>0, but two have not 5-x²>0.

So the two solutions:
(sqrt(21)-1)/2 and (1-sqrt(17))/2