Question

giúp e câu 1 ạ

Answer 1

1.a) ĐKXĐ: \(x>0,x\ne25\)

b) \(A=\left(\dfrac{1}{\sqrt{x}+5}+\dfrac{1}{\sqrt{x}-5}\right)\left(1+\dfrac{5}{\sqrt{x}}\right)\)

\(=\dfrac{\sqrt{x}-5+\sqrt{x}+5}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}.\dfrac{\sqrt{x}+5}{\sqrt{x}}=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}.\dfrac{\sqrt{x}+5}{\sqrt{x}}\)

\(=\dfrac{2}{\sqrt{x}-5}\)

c) Để \(A\in Z\Rightarrow\dfrac{2}{\sqrt{x}-5}\in Z\) mà x nguyên \(\Rightarrow\sqrt{x}-5\inƯ\left(2\right)\)

\(\Rightarrow\sqrt{x}-5\in\left\{1;2;-1;-2\right\}\Rightarrow x\in\left\{36;49;16;9\right\}\)