Question

EX 36!!AJUTOR VA ROG

Answer 1

Explicație pas cu pas:

36.

$a = {5}^{2n + 1} \cdot {4}^{3n + 2} + {10}^{2n + 1} \cdot {2}^{4n + 1} \\= 5 \cdot {5}^{2n} \cdot {4}^{2} \cdot {( {2}^{2} )}^{3n} + 10 \cdot {10}^{2n} \cdot 2 \cdot {2}^{4n}\\ = 80 \cdot {5}^{2n} \cdot {2}^{2n} \cdot {2}^{4n} + 20 \cdot {10}^{2n} \cdot {2}^{4n} \\= 80 \cdot {(5 \cdot 2)}^{2n} \cdot {2}^{4n} + 20 \cdot {10}^{2n} \cdot {2}^{4n} \\= {10}^{2n} \cdot {2}^{4n} \cdot (80 + 20) = {({10}^{n})}^{2} \cdot {({2}^{2n})}^{2} \cdot {10}^{2} \\ = {\Big[ {10}^{n + 1} \cdot {2}^{2n} \Big]}^{2}$

Answer 2

$\it a=5^{2n}\cdot5\cdot4^{3n}\cdot4^2+10^{2n}\cdot10\cdot2^{4n}\cdot2=(5^n)^2\cdot5\cdot(2^2)^{3n}\cdot16+\\ \\ +2^{2n}\cdot5^{2n}\cdot2^{4n}\cdot20=(5^n)^2\cdot(2^{3n})^2\cdot80+(5^n)^2\cdot(2^{3n})^2\cdot20=\\ \\ =(5^n)^2\cdot(8^{n})^2\cdot80+(5^n)^2\cdot(8^{n})^2\cdot20=(40^n)^2(80+20)=\\ \\ =(40^n)^2\cdot100=(40^n)^2\cdot10^2=(10\cdot40^n)^2\ \longrightarrow\ p\breve atrat\ \ perfect$