Fun little math problem

05092016, 07:24 PM
Post: #1




Fun little math problem
I was at a high school reunion this weekend and former teacher of mine gave me this little gem. It isn't hard to solve, but it's interesting that there is exactly one solution.
Find two positive numbers such that:


05092016, 08:29 PM
Post: #2




RE: Fun little math problem
1+sqrt(2), 1+(sqrt(2))/2


05092016, 10:00 PM
(This post was last modified: 05102016 05:33 AM by Tugdual.)
Post: #3




RE: Fun little math problem
I also have \(1\frac { \sqrt { 2 } }{ 2 } \) and \(1\sqrt { 2 } \)
Thanks 50G Ooops sorry it was said positive numbers. Only one solution then. 

05102016, 09:17 AM
(This post was last modified: 05102016 11:05 AM by BarryMead.)
Post: #4




RE: Fun little math problem
(05092016 08:29 PM)Gerson W. Barbosa Wrote: 1+sqrt(2), 1+(sqrt(2))/2 I think you misplaced a parenthesis, and that you meant to say 1 + sqrt(2), 1 + (sqrt(2)/2) I admit that the operator precedence rules for most computer languages would perform the division operation before the addition operation anyway, but I think most people would agree that the meaning is more clear if the parentheses are arranged as shown in the second example. Take Care, Barry 

05102016, 11:11 AM
(This post was last modified: 05102016 11:14 AM by Gerson W. Barbosa.)
Post: #5




RE: Fun little math problem
(05102016 09:17 AM)BarryMead Wrote:(05092016 08:29 PM)Gerson W. Barbosa Wrote: 1+sqrt(2), 1+(sqrt(2))/2 Actually only one pair of parentheses would have been enough: 1 + sqrt(2)/2. But redundant parentheses wouldn't hurt: (1+((sqrt(2))/2)) This is better: \(1+\frac { \sqrt { 2 } }{ 2 } \) Gerson. 

05102016, 11:14 AM
Post: #6




RE: Fun little math problem
Gerson,
Quote the reply and see how it is done. Then create your own response. \(1+\frac 1 { \sqrt { 2 } } \) Pauli 

05102016, 11:19 AM
Post: #7




RE: Fun little math problem  
05102016, 11:31 AM
(This post was last modified: 05102016 11:32 AM by Gerson W. Barbosa.)
Post: #8




RE: Fun little math problem
(05092016 10:00 PM)Tugdual Wrote: I also have \(1\frac { \sqrt { 2 } }{ 2 } \) and \(1\sqrt { 2 } \) I didn't take a 50g for this one, but I did use the wp34s to solve a quadratic equation: 1 ENTER 2 +/ 1 +/ SLVQ > 2.41421356237 x<>y > .414213562373⁻¹ Gerson. 

05102016, 03:08 PM
Post: #9




RE: Fun little math problem
Thanks for playing folks. It's interesting to graph to two functions also. You'll see that there is a limit to the solution at (0,0). Hmm. I'm sure I have the terminology wrong there, but the x+y=x*y has a solution at (0,0) and xyy/x = epsilon as x,y approach 0 (for the right small values of x&y)


05102016, 05:07 PM
(This post was last modified: 05102016 05:08 PM by Gerson W. Barbosa.)
Post: #10




RE: Fun little math problem
(05102016 03:08 PM)David Hayden Wrote: Thanks for playing folks. It's interesting to graph to two functions also. You'll see that there is a limit to the solution at (0,0). Hmm. I'm sure I have the terminology wrong there, but the x+y=x*y has a solution at (0,0) and xyy/x = epsilon as x,y approach 0 (for the right small values of x&y) Nice little problem. Thanks for posting! It reminds me of another one, workedout allegedly in half a minute by a 14year old student, about one hundred years ago: \(\left \{ _{\sqrt{y}+x=11}^{\sqrt{x}+y=7} \right.\) No ordinary student, though. Gerson. 

05102016, 05:22 PM
Post: #11




RE: Fun little math problem
These are too easy if you sit in front of a computer.


05102016, 06:11 PM
Post: #12




RE: Fun little math problem  
05102016, 06:58 PM
Post: #13




RE: Fun little math problem
(05102016 05:07 PM)Gerson W. Barbosa Wrote:I could NUM.SLV it but no chance with CAS on the 50g, keeps saying "not exact system" whatever this means...(05102016 03:08 PM)David Hayden Wrote: Thanks for playing folks. It's interesting to graph to two functions also. You'll see that there is a limit to the solution at (0,0). Hmm. I'm sure I have the terminology wrong there, but the x+y=x*y has a solution at (0,0) and xyy/x = epsilon as x,y approach 0 (for the right small values of x&y) 

05102016, 08:22 PM
(This post was last modified: 05102016 08:23 PM by Gerson W. Barbosa.)
Post: #14




RE: Fun little math problem  
05102016, 08:25 PM
(This post was last modified: 05102016 08:31 PM by Massimo Gnerucci.)
Post: #15




RE: Fun little math problem
(05102016 06:58 PM)Tugdual Wrote: I could NUM.SLV it but no chance with CAS on the 50g, keeps saying "not exact system" whatever this means... Do you really need a calc for this one? Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05102016, 09:13 PM
(This post was last modified: 05102016 09:17 PM by Tugdual.)
Post: #16




RE: Fun little math problem
(05102016 08:22 PM)Gerson W. Barbosa Wrote:I used [5 5] and it does work for NUM.SLV but the error is returned with the standard SOLVE.(05102016 06:58 PM)Tugdual Wrote: I could NUM.SLV it but no chance with CAS on the 50g, keeps saying "not exact system" whatever this means... (05102016 08:25 PM)Massimo Gnerucci Wrote: Do you really need a calc for this one?Why not? This is kind of a cal forum here... 

05102016, 09:43 PM
(This post was last modified: 05102016 09:59 PM by Massimo Gnerucci.)
Post: #17




RE: Fun little math problem
(05102016 09:13 PM)Tugdual Wrote:(05102016 08:25 PM)Massimo Gnerucci Wrote: Do you really need a calc for this one?Why not? This is kind of a cal forum here... Of course you may, but do you use one when you see 1+2+3=? :) Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05102016, 10:45 PM
Post: #18




RE: Fun little math problem  
05112016, 06:31 AM
Post: #19




RE: Fun little math problem
(05102016 10:45 PM)Paul Dale Wrote: I got the answer without a calculation aid in well under thirty seconds. How did you do it? I have to admit I only got a (very) quickanddirty solution: Since x=(7–y)² and y=(11–x)² I assumed x and y to be the squares of integers, i.e. 4 or 9 or 16, etc. A simple substitution yields 22x – x² – sqrt x = 114. Omitting the root as the smallest term yields x = 11 ± sqrt 7, i.e 8,35 and 13,65. So two candidates are 9 and 16. I first tried x=9, et voilà... #) Dieter 

05112016, 07:57 AM
Post: #20




RE: Fun little math problem  
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