Question

tim x thuoc N de bieu thuc sau co gia tri la so tu nhien: Q=\(\dfrac{\text{x}+1}{\text{x}-\sqrt{\text{x}}+1}\)

Answer 1

Ta có :

\(Q=\dfrac{x+1}{x-\sqrt[]{x}+1}\left(x\inℕ\right)\)

\(\Leftrightarrow Q=\dfrac{\left(x+1\right)\left(\sqrt[3]{x}+1\right)}{\left(\sqrt[3]{x}+1\right)\left(x-\sqrt[]{x}+1\right)}\)

\(\Leftrightarrow Q=\dfrac{\left(x+1\right)\left(\sqrt[3]{x}+1\right)}{\left(x+1\right)}\)

\(\Leftrightarrow Q=\sqrt[3]{x}+1\)

Để \(Q\inℕ\)

\(\Leftrightarrow\sqrt[3]{x}+1\inℕ\)

\(\Leftrightarrow\sqrt[3]{x}\inℕ\)

\(\Leftrightarrow x=\left\{x\inℕ|x=k^3;k\inℕ\right\}\)