BdMO Online Forum

1. $2x^2 - 8x + 7$ ei rashi'r sorbocho maan koto?
My Attempt: I firstly turned into this: 2x(x-4)+7 . Then I placed different numbers instead of $x$. Then find that it is -1 . Is it true. Is there any smarter solution?


2. $x$ er $\Re$ maan ber koro jekhane x nicher equation satisfy kore:
\[3^x + 4^x = 5^x\]

3.$2^4 \times 5^5 \times 10^8$ ei rashite koyti onko ache?
MyAttempt: if we simplyfy $10^8$ to 5 and 2 , then we get : $10^12 \times 5$ And thus the ans is 13! is ti correct?

4. $3^a - 7^b - 1=0$ ei rashir koiti somadhan ase?(very difficult to me)

5.How many subset does this set have $A$ = $\{$ 1,2,3,.....,2003$\}$ .the sum of the elements containing in that subset must be $2007000$.

6. n er koyti purno dhonattok maaner jonno $n^2 - 14n + 24$ 1ti Prime number? (ami sudhu jani prime odd hoy(except 2))

7. n ke 3 diye bhag korle 1 thake, 4diye bhag kore 2 thake, 5 diye bhag korle 3 thake, 6 diye korle 4 thake. 7 diye bhag korle koto bhagsesh thakbe? (pattern dekhe mone hoy 5 hote pare. Kintu 5 diye bhag korle 3 thake. Tai mone hoche 7 diye bhag korle 0 thakbe, kintu prosner sathe milale tao hoy na. )

1. try to make a square and use the idea that the square of a real number is always $\geq 0$.
2. Already replied. But from next time please don't double post.
3. yes, correct!
4. I don't understand your problem 4. Have you written it correctly?
5. $\dfrac{2003\times (2003+1)}{2} = 2 007 006$. Does it help?
6. I guess you should learn some number theory. Read my article on number theory http://www.kmcbd.org/Home/documents (Introduction to Number theory_KMC (By Tarik Adnan Moon).pdf)

5. 0o0o0o0o. Very easy. Just 1. But if we consider proper subset, the result is 0. And would I know that 2003*(2003+1) / 2 = 200700. Jodi bolto sum hobe 200400! tahole?

4. was set in BdMO(Div) Comilla 2008 #1.
it says " $a$ and $b$ $\Re$ hole nicher somikoroner koyti somadhan ache? $3^a -7^b -1 = 0$ "

1. ultimately to amake oi 1,2,3..... bosiye dekhte hobe!

hey, prob 2 kothay reply korso?

তুমিই তো পোস্ট করছিলা আলাদাভাবে
viewtopic.php?f=8&t=65
এজন্যই তো বলছি:>>>Already replied. But from next time please don't double post.

7no::
$3a+1=n=4b+2,theke n{1}=10,22,...........................[10+g12]..{g purnosongkha}$
$n{1}=5c+3$ er jonno 58,118.......{(5x-1)12+10}[n{1} hotee dhara toiri koree]$
${(5x-1)12+10}$ $x=natural number$
eita ki thik ase????????????????

Moon wrote:1. try to make a square and use the idea that the square of a real number is always $\geq 0$.
2. Already replied. But from next time please don't double post.
3. yes, correct!
4. I don't understand your problem 4. Have you written it correctly?
5. $\dfrac{2003\times (2003+1)}{2} = 2 007 006$. Does it help?
6. I guess you should learn some number theory. Read my article on number theory http://www.kmcbd.org/Home/documents (Introduction to Number theory_KMC (By Tarik Adnan Moon).pdf)

1 no ta ki সর্বোচ্চ না সর্বনিম্ন হবে????????সর্বোচ্চ হলে তো অসীম হওয়ার কথা।

Prob 2 er ans to 2.