Question

Tìm x, y \(\in Z\) biết :

\(y\left(\sqrt{x}+3\right)=3\sqrt{x}+15\)

Answer 1

ĐKXĐ: x>=0

\(y\left(\sqrt{x}+3\right)=3\sqrt{x}+15\)

=>\(y=\dfrac{3\sqrt{x}+15}{\sqrt{x}+3}\)

Để y là số nguyên thì \(3\sqrt{x}+9+6⋮\sqrt{x}+3\)

=>\(\sqrt{x}+3\in\left\{3;6\right\}\)

hay \(x\in\left\{0;9\right\}\)

Khi x=0 thì y=15/3=5

Khi x=9 thì \(y=\dfrac{3\cdot3+15}{3+3}=\dfrac{24}{6}=4\)