Question

[Lê Nam Khánh]

Tìm x,y thuộc N biết : 25-y²=8.(x-2009)²

Answer 1

[๖ۣۜʚ๖ۣLầɞ‏‏ү•๖ۣۜ✰︵✿ĭɗσℓ❤]

Answer 2

[❥一Ǥoɗɗεşş øf iηէεℓℓεcէ︵♛╾━╤デ╦︻]

Ta có: \(25-y^2=8\left(x-2009\right)^2\)

mà\(8\left(x-2009\right)^2\ge0\Rightarrow25-y^2\ge0\left(1\right)\)

\(8\left(x-2009\right)^2⋮8\Rightarrow25-y^2⋮8\left(2\right)\)

từ\(\left(1\right),\left(2\right)\Rightarrow y^2\in\left\{1;9;25\right\}\)

\(+,y^2=1\Rightarrow8\left(x-2009\right)^2=24\Rightarrow\left(x-2009\right)^2=3\left(ktm\right)\)

\(+,y^2=9\Rightarrow8\left(x-2009\right)^2=16\Rightarrow\left(x-2009\right)^2=2\left(ktm\right)\)

\(+,y^2=25\Rightarrow8\left(x-2009\right)^2=0\Rightarrow\left(x-2009\right)^2=0\Rightarrow x-2009=0\Rightarrow x=2009\)

Vậy\(x=2009;y=5\)hoặc\(-5\)