Find largest x

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Masum
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Find largest x

Unread post by Masum » Tue Dec 07, 2010 7:46 pm

Well.I am posting the first problem here,since first problem ofcourse easy.
Find the largest $x$ such that $x+25$ divides $(x+2)^2$
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Zzzz
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Re: Find largest x

Unread post by Zzzz » Tue Dec 07, 2010 8:47 pm

here is the first reply of the first problem :) not sure... may be i have done some mistakes due to over excitement !

\[x+25|(x+2)^2\]
\[\Rightarrow x+25|x^2 + 4x + 4\]
\[\Rightarrow x+25|x^2 + 25x - 21x +4\]
\[\Rightarrow x+25|x(x+25) - 21x +4\]
\[\Rightarrow x+25| -21x +4\]
\[\Rightarrow x+25| 21(x+25) - 21x +4\]
\[\Rightarrow x+25| 529 \]

So, the highest possible value of $x+25$ is $529$

So, the largest value of $x$ is $504$
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Moon
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Re: Find largest x

Unread post by Moon » Tue Dec 07, 2010 9:02 pm

Good Job!
Zzzz, I guess, I (we all) know you. ;)
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Zzzz
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Re: Find largest x

Unread post by Zzzz » Tue Dec 07, 2010 9:22 pm

;) ...................
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