Question

‼️(dau coronă!)‼️
Determinați numerele prime a,b,c in fiecare din cazurile:
a•b•c=1771
7•a+12b=50
a^b•b^a•c=2232

^ înseamnă la puterea
Vreau rezolvare de clasa a 5a!
Repede ca rog!

Answer 1

$\displaystyle\bf\\1771=7\cdot11\cdot23,~(descompus~in~factori~primi),~deci~in~cazul~1,\\~a,~b~si~c~pot~fi~7,~11~si~23.\\7a+12b=50 \Leftrightarrow 7a=50-12b,~50=\mathcal{M}_7+1,~si~12=\mathcal{M}_7+5 \implies b=\mathcal{M}_7+3\Leftrightarrow b=7k+3,~k\in\mathbb{N}.\\dar~7k+3~este~numar~prim,~deci~7k+3~poate~fi~3,~17,...,~dar~daca~b~este~\\17,~atunci~50-12b~nu~este~numar~natural,~testam~cazul~b=3.\\b=3 \implies 50-12\cdot3 = 50 - 36 = 14 \implies~a=2.\\a~si~b~in~cazul~2,~pot~fi~2~si~3.$

$\displaystyle\bf\\in~cazul~3,~este~vorba~despre~o~banala~descompunere~in~facori~primi.\\2232=2^3\cdot3^2\cdot31,~deci~a=2,~b=3~si~c=31,~sau~a=3,~b=2~si~\\c=31.$