## Search found 153 matches

- Fri Dec 16, 2011 2:23 am
- Forum: Algebra
- Topic: two variable equations number of solution.
- Replies:
**4** - Views:
**1758**

### Re: two variable equations number of solution.

Yes, they have infinitely many solutions.

- Fri Dec 16, 2011 12:13 am
- Forum: Algebra
- Topic: two variable equations number of solution.
- Replies:
**4** - Views:
**1758**

### Re: two variable equations number of solution.

Any "More Than One" variables equation have infinitely many solutions! (If you allow Complex numbers)

- Thu Dec 15, 2011 9:18 am
- Forum: News / Announcements
- Topic: Can i post it
- Replies:
**5** - Views:
**2841**

### Re: Can i post it

যাওয়ার তো কথা। কারণ শর্টলিস্ট ২০১০ তো এখন উন্মুক্ত।

- Sun Dec 11, 2011 2:05 am
- Forum: National Math Camp
- Topic: solutions to camp exam problem
- Replies:
**28** - Views:
**8275**

### Re: solutions to camp exam problem

@Mahi: ( Both in problem 1 and Problem 6 ) Sourav was right. You can't WLOG set them to be ordered. You WLOG can only say, "either $a\ge b\ge c$ or $a\le b \le c$"

- Sat Dec 10, 2011 11:15 pm
- Forum: Algebra
- Topic: n variable nice inequality
- Replies:
**7** - Views:
**2401**

### Re: n variable nice inequality

http://www.artofproblemsolving.com/Foru ... 4&sr=posts

A walk through Functional Equation!

A walk through Functional Equation!

- Sat Dec 10, 2011 11:13 pm
- Forum: Algebra
- Topic: n variable nice inequality
- Replies:
**7** - Views:
**2401**

- Sat Dec 10, 2011 7:53 pm
- Forum: Algebra
- Topic: n variable nice inequality
- Replies:
**7** - Views:
**2401**

### Re: n variable nice inequality

Hmm, Yes.

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(Your message contains 9 characters. The minimum number of characters you need to enter is 10.)

- Sat Dec 10, 2011 5:52 pm
- Forum: Higher Secondary Level
- Topic: ধারার সমস্যা
- Replies:
**7** - Views:
**2911**

### Re: ধারার সমস্যা

$a_{4n+6} = a_{4n+7} - a_{4n+5}=a_{2n+3}-a_{2n+2}=a_{2n+1}=a_{n}$

And, given that, $a_{4n} = a_{4n+1}-a_{4n-1}$ and so $a_2 = a_3 - a_1 = a_1 - a_0 = a_0 - a_0 = 0$

$a_{2011} = a_{1005} = a_{502} = a_{124} = a_{125} - a_{123} = a_{62} - a_{61} = a_{14} - a_{30} = a_2 - a_6 = a_2 - a_0 = -a_0 = -1$

And, given that, $a_{4n} = a_{4n+1}-a_{4n-1}$ and so $a_2 = a_3 - a_1 = a_1 - a_0 = a_0 - a_0 = 0$

$a_{2011} = a_{1005} = a_{502} = a_{124} = a_{125} - a_{123} = a_{62} - a_{61} = a_{14} - a_{30} = a_2 - a_6 = a_2 - a_0 = -a_0 = -1$

- Sat Dec 10, 2011 12:17 pm
- Forum: Algebra
- Topic: n variable nice inequality
- Replies:
**7** - Views:
**2401**

### Re: n variable nice inequality

Generalization :mrgreen: : ( Reversed Cauchy ? ) \[\left(\sum_{1\leq i \leq n }{a_i^2}\right)\left(\sum_{1\leq i \leq n }{b_i^2}\right) \leq \frac{(M+m)^2}{4Mm}\left(\sum_{1\leq i \leq n }{a_i b_i}\right)^2 \] Where, $M=\max_{1\leq i \leq n }{\left\{\frac{a_i}{b_i} \right\}}$ and $m=\min_{1\leq i \l...

- Wed Dec 07, 2011 9:57 pm
- Forum: National Math Camp
- Topic: solutions to camp exam problem
- Replies:
**28** - Views:
**8275**

### Re: solutions to camp exam problem

@Sourav: You can convert .tex file to .pdf online ( Try http://www.scribtex.com/ ). Also, there are many other software to compile latex files. But you need to write them strictly ( See here: http://en.wikibooks.org/wiki/LaTeX ) and those software are really huge! I think the best option is to use T...