 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  A Reciprocal And Square Problem (Posted on 2007-07-10) Find all real pairs (p, q) satisfying the following system of equations:
ĀĀĀĀ ĀĀĀĀ ĀĀĀĀĀ ĀĀĀĀĀ p - 1/p - q2 = 0

ĀĀĀĀ ĀĀĀĀ ĀĀĀĀĀ ĀĀĀĀĀ q/p + pq = 4

 See The Solution Submitted by K Sengupta Rating: 3.5000 (2 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 1 of 7
`p-1/p=q^2 ---(1)q(p+1/p)=4 ---(2)(p+1/p)^2 - (p-1/p)^2 = 4=> (p+1/p)^2 - q^2 = q(p+1/p) (from eq(1)&eq(2))Let (P+1/p)=x, then x^2-x*q-q^2=0yields x=q(1+root(5))/2 or q(1-root(5))/2sub these in eq(2),q^2 = 8/(root(5)+1) or 8/(1-root(5))but 1-root5 is negative, so this cant be equal to q^2so q = (+/-)√(2*(√5-1))substiute q^2 = 2*(√5-1) in eq(1) to solve for pp=(+/-)(√5-1)(+/-)*√(7-2*√5)That means p can take 4 values and q can take 2 values`

 Posted by Praneeth Yalavarthi on 2007-07-10 10:15:27 Please log in:

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