## Prob!

For students of class 11-12 (age 16+)
Mathlover
Posts: 12
Joined: Thu May 12, 2011 6:05 pm

### Prob!

\[(a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})\]
express this equation as the sum of two squares.

Abdul Muntakim Rafi
Posts: 173
Joined: Tue Mar 29, 2011 10:07 pm

### Re: Prob!

\[(a^2c^2+a^2d^2+b^2c^2+b^2d^2) (e^2+f^2)\]
\[e^2(a^2c^2+a^2d^2+b^2c^2+b^2d^2)+f^2(a^2c^2+a^2d^2+b^2c^2+b^2d^2) \]

\[e^2(x^2+y^2)+f^2(x^2+y^2) \]
\[e^2x^2+e^2y^2+f^2x^2+f^2y^2 \]
\[(ex+fy)^2+(ey-fx)^2\] Man himself is the master of his fate...

Mathlover
Posts: 12
Joined: Thu May 12, 2011 6:05 pm

### Re: Prob!

thank u soooo much!!

sourav das
Posts: 461
Joined: Wed Dec 15, 2010 10:05 am
Location: Dhaka
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### Re: Prob!

Proof the general version now,\$\prod (a^{2}_{i}+a^{2}_{j})\$ can be shown as sum of two squares. (Very easy with a simple trick)
You spin my head right round right round,
When you go down, when you go down down......
(-\$from\$ "\$THE\$ \$UGLY\$ \$TRUTH\$" )

*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
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### Re: Prob!

Factorisation!

Use \$L^AT_EX\$, It makes our work a lot easier!

Abdul Muntakim Rafi
Posts: 173
Joined: Tue Mar 29, 2011 10:07 pm

### Re: Prob!

I don't understand the signs... Explain them...
Man himself is the master of his fate...

sourav das
Posts: 461
Joined: Wed Dec 15, 2010 10:05 am
Location: Dhaka
Contact:

### Re: Prob!

\$\prod_{i=1}^{n-1} (a_{i}^2 + a_{i+1}^2)=(a_{1}^2 + a_{2}^2)(a_{3}^2 + a_{4}^2).....(a_{n-1}^2 + a_{n}^2)\$
You spin my head right round right round,
When you go down, when you go down down......
(-\$from\$ "\$THE\$ \$UGLY\$ \$TRUTH\$" )

Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

### Re: Prob!

here's the crux move-if two integers are sum of two squares,then their product is also sum of two squares.
বড় ভালবাসি তোমায়,মা

*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
Contact:

### Re: Prob!

Or use complex numbers to write \$a^2+b^2=(a+bi)(a-bi)\$ and use the fact that multiplications of any two numbers in the form \$a+bi\$ or \$a-bi\$ also has that form.So it follows directly.

Use \$L^AT_EX\$, It makes our work a lot easier!

Abdul Muntakim Rafi
Posts: 173
Joined: Tue Mar 29, 2011 10:07 pm

### Re: Prob!

Thanks for telling the meaning... Sourav

and mine is like tahmid's...

\[(a^2+b^2)(c^2+d^2)\]
can be written as
We can continue in this way... 