Question

Aflati numarul natural nenul n astfel incat sa aiba loc egalitatile de mai jos:
a)n supra 3= 3 supra n
b)2 supra n=n supra 18
c)2n supra 5 =10 supra n
d)3n supra 7= 21 supra n

Answer 1

a)$\frac{n}{3} = \frac{3}{n}$n*n=(3)*(3)n²=9
n=±√9
n=3 or n=−3

b)$\frac{2}{n} = \frac{n}{18}$
(2)*(18)=n*n36=n²
36−n²=n²−n²−n²+36=0
−n²+36−36=0−36−n²=−36
$\frac{- n^{2} }{-1} = \frac{-36}{-1}$
n²=36
n=±√36n=6 or n=−6

c)$[tex] \frac{2n}{5} = \frac{10}{n}$ [/tex]
$[tex] \frac{(2n)}{5} = \frac{10}{n}$[/tex]
2n*n=(10)*(5)2n²=50 
$[tex][tex] \frac{2 n^{2} }{2} = \frac{50}{2}$[/tex][/tex]
n²=25
n=±√25n=5 or n=−5

d)$\frac{3n}{7} = \frac{21}{n}$
$[tex] \frac{(3n)}{7} = \frac{21}{n}$[/tex]
3n*n=(21)*(7)3n²=147
$[tex] \frac{3n^{2} }{3} = \frac{147}{3}$[/tex]
n²=49
n=±√49n=7 or n=−7