Subtract From Sum And Multiply, Get Number(s) (Posted on 2007-07-19)

	Submitted by K Sengupta
Rating: 3.0000 (1 votes)
Solution:	(Hide)
Multiplying both sides of the two equations and simplifying, we obtain: pq(b^2 -9b+ 8) =0, whenever b=p+q Or, pq(b-8)(b-1) = 0 Thus, p=0, or q=0, or p+q= 1, 8 We observe that p=0 gives q=0 from the two given equations. Likewise, q=0 yields p=0 Now, substituting p+q=8 in the first equation, we obtain: 4p=q, so that: (p,q) = (8/5, 32/5) Substituting p+q =1 in the first equation, we obtain: 16p+3q =0, so that: (p, q) = (-3/13, 16/13) Consequently, (p, q) = (0,0); (8/5, 32/5); (-3/13, 16/13) constitutes all possible solutions to the given problem.

	Subject	Author	Date
	Quick	Federico Kereki	2007-07-20 08:17:25
	re: Solution	xdog	2007-07-19 22:13:14
	Solution	Praneeth Yalavarthi	2007-07-19 10:00:09