## 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
Replies: 4
Views: 4992

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
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 $n \in\mathbb N$.