Question

Tìm \(x\) thuộc \(Z\) để \(A\) thuộc \(Z\):

\(A=\dfrac{\text{√}x+1}{\text{√}x-3}\)

Answer 1

\(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}=\dfrac{\sqrt{x}-3+4}{\sqrt{x}-3}=1+\dfrac{4}{\sqrt{x}-3}\)

A nguyên khi \(4⋮\sqrt{x}-3\)

\(\Rightarrow\sqrt{x}-3=\left\{-4;-2;-1;1;2;4\right\}\)

\(\sqrt{x}-3\)	-4	-2	-1	1	2	4
x	\(\varnothing\)	1	4	16	25	49

vậy khi x={1;4;16;25} thì A nguyên

Answer 2

Để A thuộc Z thì \(\sqrt{x}+1⋮\sqrt{x}-3\)

\(\Rightarrow\sqrt{x}-3+4⋮\sqrt{x}-3\)

mà \(\sqrt{x}-3⋮\sqrt{x}-3\Rightarrow4⋮\sqrt{x}-3\)

\(\Rightarrow\sqrt{x}-3\inƯ\left(4\right)\)

\(\Rightarrow\sqrt{x}-3\in\left\{\pm1;\pm2;\pm4\right\}\)

Xét các th...