Question

Tìm \(x\in Z\) để \(\frac{8}{\sqrt{x}+5}\) nhận giá trị nguyên

Answer 1

\(\sqrt{x}\ge0\Rightarrow\sqrt{x}+5\ge5\)

\(\frac{8}{\sqrt{x}+5}\in Z\Leftrightarrow8⋮\sqrt{x}+5\Leftrightarrow\sqrt{x}+5\inƯ\left(8\right)=\left\{8\right\}\)

roi giai ra x = 

Answer 2

Để \(\frac{8}{\sqrt{x}+5}\in Z\) <=> \(8⋮\sqrt{x}+5\)

<=> \(\sqrt{x}+5\)\(\in\)Ư(8) = {1; -1; 2; -2; 4; -4; 8; -8}

Do \(\sqrt{x}\ge0\) => \(\sqrt{x}+5\ge5\)

 => \(\sqrt{x}+5=8\)

=> \(\sqrt{x}=8-5\)

=> \(\sqrt{x}=3\)

=> \(x=9\)