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
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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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
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learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Find largest x
...................
Every logical solution to a problem has its own beauty.
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