MHB What is x when c is at maximum?

  • Thread starter Thread starter Wilmer
  • Start date Start date
  • Tags Tags
    Puzzle
Click For Summary
The discussion revolves around solving the equations a = x^2 + 2cx + 1 and b = 2x + 3c + 3, with the condition that a/b = 5 plus a remainder of 11. The solution for c is found to be -10 when x equals 25, with a total of six integer solutions for c and x. Among these, three solutions have both x and c as positive integers. The main inquiry shifts to determining the value of x when c is at its maximum. The conversation indicates a collaborative effort to explore these mathematical relationships for a puzzle site.
Wilmer
Messages
303
Reaction score
0
a = x^2 + 2cx + 1
b = 2x + 3c + 3

a / b = 5 plus a remainder of 11.

c=?

Want to include above in a "puzzle" site.
Want see if it makes sense..

Can you solve it?
Than you.
 
Mathematics news on Phys.org
Wilmer said:
...Can you solve it?...

Yes:

One easy solution is:

$$c=-10$$

I will be glad to show what I did if required.
 
MarkFL said:
Yes:
One easy solution is:
$$c=-10$$
I will be glad to show what I did if required.
Yippee! Yes, c=-10 (x=25) is a solution.

There are 6 solutions (I'm 99% sure) where c and x are integers (positive or negative).
3 of those have x and c > 0.

Hokay: question is now: what is x when c is at maximum?

Thanks Mark. Nice to hear from you !
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

A What are your insights on The Hardest Logic Puzzle Ever?
Replies
2
Views
2K
MHB Solve Polynomial Scale: Find a,b,c,d
Replies
4
Views
2K
MHB Find the amount of sand in each bag
Replies
1
Views
1K
MHB Find Polynomial Given Remainder After Division
Replies
6
Views
2K
MHB Which procedure takes the minimum time to solve modulus functions?
Replies
5
Views
1K
MHB Linear combination of sine and cosine function
Replies
3
Views
2K
MHB [ASK] polynomial f(x) divided by (x - 1)
Replies
2
Views
2K
MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
Replies
1
Views
1K
MHB Did I Calculate My Funds Distribution Correctly?
Replies
2
Views
1K
Challenge VI: 15 Puzzle solved by Boorglar and mfb
Replies
9
Views
4K

Hot Threads

Recent Insights

Back
Top