Question

10. Determinati numerele naturale n pentru care:
a) n supra 3<2 supra 3
b)7 supra 4>4n+5 supra 4
c)7 supra n>7 supra 2
d)11 supra 17<11 supra 5n+4

un rasouns CORECT si bine formulat primeste inima, 5 stele si o coroana, repede va rog​

Answer 1

Răspuns:

a)n=1; 1pe3<2pe3;

b)n=0;4n=4×n; 7pe4>4×0+5pe4; 7pe4>5pe4;

c)n=1;7pe1>7pe2;

d)n=2;11pe17<11pe5×2+4; 11pe17<11pe14;

Answer 2

$\it a)\ \ \dfrac{n}{3}<\dfrac{2}{3}\ \Rightarrow n<2 \Rightarrow n\in\{0,\ 1\}\\ \\ \\ b)\ \dfrac{7}{4}>\dfrac{4n+5}{4} \Rightarrow 7 > 4n+5 \Rightarrow 4n+5<7|_{-5} \Rightarrow 4n<2\Rightarrow n=0\\ \\ \\ c)\ \dfrac{7}{n}>\dfrac{7}{2} \Rightarrow \dfrac{n}{7}<\dfrac{2}{7} \Rightarrow n<2 \Rightarrow n\in\{0,\ 1\}$

$\it \dfrac{11}{17}<\dfrac{11}{5n+4} \Rightarrow \dfrac{17}{11}>\dfrac{5n+4}{11} \Rightarrow 17 > 5n+4 \Rightarrow 5n+4<17|_{-4} \Rightarrow\\ \\ \\ \Rightarrow 5n < 13 \Rightarrow n \in \{0,\ 1,\ 2 \}$