Question

[Tiên Phạm]

Giúp mình câu 2 và câu 4

Answer 1

[Hồng Phúc]

1.

ĐK: \(x\ge0;x\ne9\)

\(Q=-\dfrac{1}{\sqrt{x}-3}\in Z\)

\(\Leftrightarrow\sqrt{x}-3\inƯ_1=\left\{\pm1;\pm3\right\}\)

\(\Leftrightarrow\sqrt{x}\in\left\{0;2;4;6\right\}\)

\(\Leftrightarrow x\in\left\{0;4;16;36\right\}\)

Answer 2

[Hồng Phúc]

2.

ĐK: \(x\ge0;x\ne1\)

\(Q=\dfrac{\sqrt{x}-3}{\sqrt{x}-1}\in Z\)

\(\Leftrightarrow1-\dfrac{2}{\sqrt{x}-1}\in Z\)

\(\Leftrightarrow\sqrt{x}-1\inƯ_2=\left\{\pm1;\pm2\right\}\)

\(\Leftrightarrow\sqrt{x}\in\left\{0;2;3\right\}\)

\(\Leftrightarrow x\in\left\{0;4;9\right\}\)