Question

Answer 1

a: ĐKXĐ: x>1

\(P=2\cdot\dfrac{\sqrt{x-1}+1-\sqrt{x-1}}{\sqrt{x-1}\left(\sqrt{x-1}+1\right)}:\dfrac{\sqrt{x}-1}{x-1+\sqrt{x-1}}\)

\(=2\cdot\dfrac{1}{\sqrt{x-1}\left(\sqrt{x-1}+1\right)}\cdot\dfrac{x-1+\sqrt{x-1}}{\sqrt{x}-1}\)

\(=\dfrac{2}{x-1+\sqrt{x-1}}\cdot\dfrac{x-1+\sqrt{x-1}}{\sqrt{x}-1}=\dfrac{2}{\sqrt{x}-1}\)

b: P là số nguyên

=>căn x-1 thuộc {1;-1;2;-2}

mà x>1

nên x thuộc {4;9}