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        riddles >> medium >> Help
        
(Message started by: Rkiuyto on Dec 31^st, 2008, 1:19am)

Title: Help
Post by Rkiuyto on Dec 31^st, 2008, 1:19am

1. Find the value of
tan² 1+ tan² 3+......+tan² 89.

2.Find the ordered pairs x and y where x and y are real numbers such that x and y satisfy the two equations below.

(1/sqrt x)+(1/sqrt y)=(x+3y)(3x+y)
(1/sqrt x)-(1/sqrt y)=2 (y²-x²)

Title: Re: Help
Post by towr on Dec 31^st, 2008, 1:25am

1) http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1199866905;

Title: Re: Help
Post by 1337b4k4 on Jan 12^th, 2009, 7:26pm

2.) [hide] case 1: x = y. Then we get 2/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gifx = 16xhttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sup2.gif, or x = y = 2 ^ (-6/5)
case 2: x != y. More to come hopefully?[/hide]