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resoudre-dans-N-2-l-equation-2x-2-3y-2-35-




Question Number 206636 by mathzup last updated on 21/Apr/24
resoudre dans N^2   l equation  2x^2 +3y^2 =35
$${resoudre}\:{dans}\:{N}^{\mathrm{2}} \:\:{l}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} =\mathrm{35} \\ $$
Commented by A5T last updated on 21/Apr/24
(x,y)=(4,1)  x∈N⇒2≤2x^2 ≤35⇒ 1≤x≤4, then check.
$$\left({x},{y}\right)=\left(\mathrm{4},\mathrm{1}\right) \\ $$$${x}\in\mathbb{N}\Rightarrow\mathrm{2}\leqslant\mathrm{2}{x}^{\mathrm{2}} \leqslant\mathrm{35}\Rightarrow\:\mathrm{1}\leqslant{x}\leqslant\mathrm{4},\:{then}\:{check}. \\ $$

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