Ecuatie cu numere naturale

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salazar
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Ecuatie cu numere naturale

Post by salazar »

Rezolvati in multimea nr. naturale ecuatia:
\( 4m^2+4n=n^2+4m+11 \).

G.M 3/2009
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Mateescu Constantin
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Post by Mateescu Constantin »

Ecuatia se scrie:
\( 4m^2-4m+1=n^2-4n+4+8 \)
\( \Longleftrightarrow (2m-1)^2=(n-2)^2+8 \)
\( \Longleftrightarrow (2m-1+n-2)(2m-1-n+2)=8 \)

De aici e simplu.
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