Question

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne1\end{matrix}\right.\)

Để P nguyên thì \(\sqrt{x}+3⋮\sqrt{x}-1\)

=>\(\sqrt{x}-1+4⋮\sqrt{x}-1\)

=>\(4⋮\sqrt{x}-1\)

mà \(\sqrt{x}-1>=-1\forall x\) thỏa mãn ĐKXĐ

nên \(\sqrt{x}-1\in\left\{-1;1;2;4\right\}\)

=>\(\sqrt{x}\in\left\{0;2;3;5\right\}\)

=>\(x\in\left\{0;4;9;25\right\}\)