## Search found 188 matches

- Wed Oct 03, 2012 3:15 pm
- Forum: Secondary Level
- Topic: $3^{x}+4^{y}=5^{z}$
- Replies:
**1** - Views:
**1064**

### $3^{x}+4^{y}=5^{z}$

Find all integer solution of the equation, $3^{x}+4^{y}=5^{z}$ .

- Fri Sep 28, 2012 12:27 pm
- Forum: Higher Secondary Level
- Topic: Quad in square
- Replies:
**4** - Views:
**4992**

### Re: Quad in square

We will use a simple lemma to prove it. Lemma : In any right angled triangle with the sides $a,b,c$ where $c$ is a hypotenuse.Then $\sqrt{2}c \geq a+b$.(Prove the lemma yourself by $A.M-G.M$.) Now applying it in $\Delta EBF$, we get, $\sqrt{2}EF \geq EB+BF$. Likewise,$\sqrt{2}FG \geq FC+CG$,$\sqrt{2...

- Wed Sep 26, 2012 4:48 pm
- Forum: Introductions
- Topic: Need Suggestion please
- Replies:
**8** - Views:
**4126**

### Re: Need Suggestion please

Can I have Aiyub vai's E-mail ID or facebook name? Anyway,Thank you very much for the help to both of you. . I was struggling actually.

- Wed Sep 26, 2012 2:21 pm
- Forum: Secondary Level
- Topic: Square roots.
- Replies:
**0** - Views:
**827**

### Square roots.

Find all positive real $x$ such that, $\sqrt{x}+\frac{1}{\sqrt{x}} \in \mathbb N$.

- Tue Sep 18, 2012 10:42 pm
- Forum: Introductions
- Topic: Need Suggestion please
- Replies:
**8** - Views:
**4126**

### Re: Need Suggestion please

I also need help... from where I can get those books? Most of the foreign books are not found easily.Even I haven't read most of these books.My only support is some Problem books in bengali like 'অলিম্পিয়াড সমগ্র" etc.

- Wed Sep 12, 2012 12:48 pm
- Forum: Algebra
- Topic: Which way to go?
- Replies:
**3** - Views:
**1192**

### Re: Which way to go?

Sorry for the foolish typo. I hate latexing, I had to edit 4 times in total!

- Tue Sep 11, 2012 2:14 pm
- Forum: Algebra
- Topic: Which way to go?
- Replies:
**3** - Views:
**1192**

### Re: Which way to go?

At first I thought the problem would require some serious theorems.But my thought got in vain.You know,I know a little in inequalities though I tried what my best to find it with simple way. $8(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})+9 \geq 10(x^{2}+y^{2}+z^{2})$ $\rightarrow8(xy+yz+zx)+9xyz \geq 10(x^...

- Mon Sep 03, 2012 11:45 pm
- Forum: Secondary Level
- Topic: Prime or Composite
- Replies:
**2** - Views:
**1137**

### Re: Prime or Composite

I solved the same problem a month ago and i did like this....

- Mon Sep 03, 2012 3:23 pm
- Forum: Junior Level
- Topic: সহজ থেকেও সহজতর
- Replies:
**2** - Views:
**1583**

### Re: সহজ থেকেও সহজতর

Sorry,forgot to give the condition .

The fact killed the solution actually

The fact killed the solution actually

- Fri Aug 31, 2012 4:34 pm
- Forum: Junior Level
- Topic: সহজ থেকেও সহজতর
- Replies:
**2** - Views:
**1583**

### সহজ থেকেও সহজতর

প্রমাণ কর, $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+3}$ একটি পৌনঃপুনিক(Repeated decimal) সংখ্যা যেখানে $n \in\mathbb N$.