Question

5 ,6 cine scris primul dau coroana♡!!!

Answer 1

Răspuns

Explicație pas cu pas:

$\dfrac{3\cdot 7^n+7^{n+1}}{7^{n+1}+5\cdot 7^{n+2}}= \dfrac{7^n(3+7)}{7^n(7+5\cdot 7^2)}=\dfrac{10}{7+5\cdot 49 } = \dfrac{10}{252}\\\dfrac{5\cdot 3^{n+1}-2\cdot 3^n}{3^{n+1}+4\cdot 3^{n+2}}= \dfrac{3^n(5\cdot 3-2)}{3^n(3+4\cdot 3^2)}=\dfrac{15-2}{3+4\cdot 9}=\dfrac{13}{39}= \dfrac{1}{3} \\\dfrac{10}{252} : \dfrac{1}{3} = \dfrac{10}{252} \cdot 3 = \dfrac{10}{84}=\dfrac{5}{42} ,deci~de~\dfrac{5}{42}~ori\\\\\dfrac{a}{b}=\dfrac{3}{5}\Rightarrow \dfrac{a}{3}=\dfrac{b}{5}= k\Rightarrow a=3k,b=5k$

$N=n\cdot a\cdot b=n\cdot 3k\cdot 5k=n\cdot 3\cdot 5\cdot k^2\\\text{Deoacere }(3,5)=1 \Rightarrow n=3\cdot 5 = 15$