Question

Mulțimea numerelor naturale n pentru care fracția n+1/3n+4 este ireductibilă:A:{0,1,2}
B:N
C:{1,2,3,5}
D:{0,1,2,3,4,5}​
AM NEVOIE URGENT

Answer 1

Răspuns: Varianta B) n ∈ IN

Explicație pas cu pas:

Salutare!

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$\bf \dfrac{n+1}{3n+4} \longrightarrow fractie~ireductibila$  

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$\bf \underline{n=0} \implies \dfrac{0+1}{3\cdot 0+4} = \dfrac{1}{4} \longrightarrow fractie~ireductibila$

$\it~~~$

$\bf \underline{n=1} \implies \dfrac{1+1}{3\cdot 1+4} = \dfrac{1}{7} \longrightarrow fractie~ireductibila$

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$\bf \underline{n=2} \implies \dfrac{2+1}{3\cdot 2+4} = \dfrac{3}{10} \longrightarrow fractie~ireductibila$

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$\bf \underline{n=3} \implies \dfrac{3+1}{3\cdot 3+4} = \dfrac{4}{13} \longrightarrow fractie~ireductibila$

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$\bf \underline{n=4} \implies \dfrac{4+1}{3\cdot 4+4} = \dfrac{5}{16} \longrightarrow fractie~ireductibila$

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$\bf \underline{n=5} \implies \dfrac{5+1}{3\cdot 5+4} = \dfrac{6}{19} \longrightarrow fractie~ireductibila$

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$\text{\bf Observam ca fractia e ireductibila pentru}~\bf \underline{n\in \mathbb{N}}$

Varianta B) n ∈ IN

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