Question

Determinaţi numerele naturale nenulex si y , stiind ca
x/2=y² si x/4=4·y

Answer 1

[tex]\it \dfrac{x}{2}=y^2 \Longrightarrow x = 2y^2\ \ \ \ (1) \\\;\\ \\\;\\ \dfrac{x}{4} = 4y \Longrightarrow x = 16y\ \ \ \ (2) \\\;\\ \\\;\\ (1),\ (2) \Longrightarrow 2y^2=16y|_{:2} \Longrightarrow y^2 = 8y \Longrightarrow y^2-8y=0 \Longrightarrow [/tex]

[tex]\it \Longrightarrow y(y-8) = 0 \Longrightarrow \begin{cases} \it y_1 = 0 \ \ \ \ (3) \\\;\\ \it y-8=0 \Longrightarrow y_2 = 8\ \ \ \ (4) \end{cases}[/tex]

[tex]\it (2),\ (3) \Longrightarrow x = 0 \\\;\\ (2), (4) \Longrightarrow x = 128 \\\;\\ Deci,\ (x,\ y)\in \{(0,\ 0),\ (128,\ 8)\}[/tex]