Well.I am posting the first problem here,since first problem ofcourse easy.

Find the largest $x$ such that $x+25$ divides $(x+2)^2$

## Find largest x

### Find largest x

One one thing is neutral in the universe, that is $0$.

### Re: Find largest x

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 $504$

\[x+25|(x+2)^2\]

\[\Rightarrow x+25|x^2 + 4x + 4\]

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

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

\[\Rightarrow x+25| -21x +4\]

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

\[\Rightarrow x+25| 529 \]

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

So, the largest value of $x$ is $504$

Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Find largest x

Good Job!

Zzzz, I guess, I (we all) know you.

Zzzz, I guess, I (we all) know you.

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.### Re: Find largest x

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Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)