la 31 si 32 va rog repedeeee

La 31 o iei si tu prin incercari.
pt n=2 => 8/18 , dar suma nu face 52
n=3 =>12/27, dar suma nu face 52
n=4 => 16/36, si uite ca 16+36 face 52.

Iar 32 mi se pare putin dubios, ori nu sunt eu in stare sa vad ceva simplu, ori e enuntul gresit....

Cel mai mic numar cu care poti sa le simplifici cat sa iti dea o fractie naturala este 5, si o sa obtii 24/15 , dar diferenta lor nu face 6. Apoi o mai simplifici cu 3 si face 8/5 , dar diferenta nu face 6....

Tcostel Tcostel · Answer 2 · 2017-08-22T12:43:49+03:00

[tex]\displaystyle\\ 31)\\\\ \frac{4}{9} ~~\text{(amplificata cu n)} = \frac{4n}{9n} \\\\ 4n+9n = 52\\\\ 13n = 52\\\\ n = \frac{52}{13} = \boxed{\bf 4} [/tex]

[tex]\displaystyle\\ 32)\\\\ \frac{120}{75} ~~\text{(simplificata cu n)} = \frac{120:n}{75:n} = \frac{ \dfrac{120}{n}}{ \dfrac{75}{n}} \\\\ \frac{120}{n}-\frac{75}{n} = 6\\\\ \frac{120-75}{n}=6\\\\ \frac{45}{n}=6\\\\ n = \frac{45}{6} = \frac{15}{2} = 7,5 \notin N \\\\ \Longrightarrow ~~\text{Problema are o greseala de tipar.}\\\text{Probabil diferenta dintre numarator si numitor = 9 in loc de 6. }\\\\ \text{Refacem calculele pentru diferenta = 9} [/tex]

[tex] \displaystyle \\ \frac{120}{n}-\frac{75}{n} = 9\\\\ \frac{120-75}{n}=9\\\\ \frac{45}{n}=9\\\\ n = \frac{45}{9} = \boxed{\bf 5}[/tex]